Darshan03/Edugorrila · Datasets at Hugging Face

input_text stringlengths 7 4k	input_ids sequencelengths 512 512	attention_mask sequencelengths 512 512
20 Democratic Politics When the demand for the formation of States on the basis of language was raised, some national leaders feared that it would lead to the disintegration of the country. The Central Government resisted linguistic States for some time. But the experience has shown that the formation of linguistic States has actually made the country, more united. It has also made administration easier. Language policy A second test for Indian federation is the language policy. Our Constitution did not give the status of national language to any one language. Hindi was identified as the official language. But Hindi is the mother tongue of only about 40 per cent of Indians. Therefore, there were many safeguards to protect other languages. Besides Hindi, there are 21 other languages recognised as Scheduled Languages by the Constitution. A candidate in an examination conducted for the Central Government positions may opt to take the examination in any of these languages. States too have their own official languages. Much of the government work takes place in the official language of the concerned State. Unlike Sri Lanka, the leaders of our country adopted a very cautious attitude in spreading the use of Hindi. According to the Constitution, the use of English for official purposes was to stop in 1965. However, many non- Hindi speaking States demanded that the use of English continue. In Tamil Nadu, this movement took a violent form. The Central Government responded by agreeing to continue the use of English along with Hindi for official purposes. Many critics think that this solution favoured the English- speaking elite. Promotion of Hindi continues to be the official policy of the Government of India. Promotion does not mean that the Central Government can impose Hindi on States where people speak a different language. The flexibility shown by Indian political leaders helped our country avoid the kind of situation that Sri Lanka finds itself in. Centre-State relations Restructuring the Centre-State relations is one more way in which federalism has been strengthened in practice. How the constitutional arrangements for sharing power work in reality depends to a large extent on how the ruling parties and leaders follow these arrangements. For a long time, the same party ruled both at the Centre and in most of the States. This meant that the State governments did not exercise their rights as autonomous federal units. As and when the ruling party at the State level was different, the parties that ruled at the Centre tried to undermine the power of the States. In those days, the Central Government would often misuse the Constitution to dismiss the State governments that were controlled by rival parties. This undermined the spirit of federalism. All this changed significantly after 1990. This period saw the rise of regional political parties in many States of the country. This was also the beginning of the era of COALITION GOVERNMENTS at the Centre. Since no single party got a clear majority in the Lok Sabha, the major national parties had to enter into an alliance with many parties including several regional parties to form a government at the Centre. This led to a new culture of power sharing and respect for the autonomy of State Governments. This trend was Coalition government A government formed by the coming together of at least two political parties. Usually partners in a coalition form a political alliance and adopt a common programme. Why Hindi? 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Science W e see a variety of objects in the world around us. However, we are unable to see anything in a dark room. On lighting up the room, things become visible. What makes things visible? During the day, the sunlight helps us to see objects. An object reflects light that falls on it. This reflected light, when received by our eyes, enables us to see things. We are able to see through a transparent medium as light is transmitted through it. There are a number of common wonderful phenomena associated with light such as image formation by mirrors, the twinkling of stars, the beautiful colours of a rainbow, bending of light by a medium and so on. A study of the properties of light helps us to explore them. By observing the common optical phenomena around us, we may conclude that light seems to travel in straight lines. The fact that a small source of light casts a sharp shadow of an opaque object points to this straight-line path of light, usually indicated as a ray of light. If an opaque object on the path of light becomes very small, light has a tendency to bend around it and not walk in a straight line an effect known as the diffraction of light. Then the straight-line treatment of optics using rays fails. To explain phenomena such as diffraction, light is thought of as a wave, the details of which you will study in higher classes. Again, at the beginning of the 20th century, it became known that the wave theory of light often becomes inadequate for treatment of the interaction of light with matter, and light often behaves somewhat like a stream of particles. This confusion about the true nature of light continued for some years till a modern quantum theory of light emerged in which light is neither a wave nor a particle the new theory reconciles the particle properties of light with the wave nature. In this Chapter, we shall study the phenomena of reflection and refraction of light using the straight-line propagation of light. These basic concepts will help us in the study of some of the optical phenomena in nature. We shall try to understand in this Chapter the reflection of light by spherical mirrors and refraction of light and their application in real life situations. A highly polished surface, such as a mirror, reflects most of the light falling on it. 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250 MATHEMATICS Solution The volume of water in the overhead tank equals the volume of the water removed from the sump. Now, the volume of water in the overhead tank (cylinder) r2h 3.14 0.6 0.6 0.95 m3 The volume of water in the sump when full l b h 1.57 1.44 0.95 m3 The volume of water left in the sump after filling the tank (1.57 1.44 0.95) (3.14 0.6 0.6 0.95) m3 (1.57 0.6 0.6 0.95 2) m3 So, the height of the water left in the sump volume of water left in the sump l b 1.57 0.6 0.6 0.95 2 m 1.57 1.44 0.475 m 47.5 cm Also, Capacity of tank Capacity of sump 3.14 0.6 0.6 0.95 1 1.57 1.44 0.95 2 Therefore, the capacity of the tank is half the capacity of the sump. Example 10 A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire. Solution The volume of the rod 2 3 3 1 8 cm 2 cm 2 . The length of the new wire of the same volume 18 m 1800 cm If r is the radius (in cm) of cross-section of the wire, its volume r2 1800 cm3 Therefore, r2 1800 2 i.e., r2 1 900 i.e., r 1 30 So, the diameter of the cross section, i.e., the thickness of the wire is 1 15 cm, i.e., 0.67mm (approx.). Example 11 A hemispherical tank full of water is emptied by a pipe at the rate of 4 37 litres per second. How much time will it take to empty half the tank, if it is 3m in diameter? 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92 MATHEMATICS 6.3 Intersecting Lines and Non-intersecting Lines Draw two different lines PQ and RS on a paper. You will see that you can draw them in two different ways as shown in Fig. 6.5 (i) and Fig. 6.5 (ii). (i) Intersecting lines (ii) Non-intersecting (parallel) lines Fig. 6.5 Different ways of drawing two lines Recall the notion of a line, that it extends indefinitely in both directions. Lines PQ and RS in Fig. 6.5 (i) are intersecting lines and in Fig. 6.5 (ii) are parallel lines. Note that the lengths of the common perpendiculars at different points on these parallel lines is the same. This equal length is called the distance between two parallel lines. 6.4 Pairs of Angles In Section 6.2, you have learnt the definitions of some of the pairs of angles such as complementary angles, supplementary angles, adjacent angles, linear pair of angles, etc. Can you think of some relations between these angles? Now, let us find out the relation between the angles formed when a ray stands on a line. Draw a figure in which a ray stands on a line as shown in Fig. 6.6. Name the line as AB and the ray as OC. What are the angles formed at the point O? They are AOC, BOC and AOB. Can we write AOC BOC AOB? (1) Yes! (Why? Refer to adjacent angles in Section 6.2) What is the measure of AOB? It is 180. (Why?) (2) From (1) and (2), can you say that AOC BOC 180? Yes! (Why?) 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Po w e r-sh a r i n g 1 Chapter I Power-sharing Overview With this chapter, we resume the tour of democracy that we started last year. We noted last year that in a democracy all power does not rest with any one organ of the government. An intelligent sharing of power among legislature, executive and judiciary is very important to the design of a democracy. In this and the next two chapters, we carry this idea of power-sharing forward. We start with two stories from Belgium and Sri Lanka. Both these stories are about how democracies handle demands for power-sharing.The stories yield some general conclusions about the need for power-sharing in democracy. 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52 CONTEMPORARY INDIA-I 2. Answer the following questions briefly. (i) What factors are responsible for the distribution of plants and animals in India? (ii) What is a bio-reserve? Give two examples. (iii) Name two animals having habitat in tropical and montane type of vegetation. 3. Distinguish between (i) Flora and Fauna (ii) Tropical Evergreen and Deciduous forests 4. Name different types of Vegetation found in India and describe the vegetation of high altitudes. 5. Quite a few species of plants and animals are endangered in India. Why? 6. Why has India a rich heritage of flora and fauna? Map Skills On an outline map of India, label the following. (i) Areas of Evergreen Forests (ii) Areas of Dry Deciduous Forests (iii) Two national parks each in Northern, Southern, Eastern and Western parts of the Country ProjectActivity (i) Find some trees in your neighbourhood having medicinal values. (ii) Find ten occupations getting raw material from forests and wildlife. (iii) Write a poem or paragraph showing the importance of wildlife. (iv) Write the script of a street play giving the importance of tree plantation and try to enact it in your locality. (v) Plant a tree either on your birthday or one of your family members birthday. 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196 India and the Contemporary World education, and returns as the judge in the local court. Meanwhile, the villagers, thinking that the landlords men had killed him, file a case. At the conclusion of the trial, the judge reveals his true identity, and the Nambuthiri repents and reforms his ways. Saraswativijayam stresses the importance of education for the upliftment of the lower castes. From the 1920s, in Bengal too a new kind of novel emerged that depicted the lives of peasants and low castes. Advaita Malla Burmans (1914-51) Titash Ekti Nadir Naam (1956) is an epic about the Mallas, a community of fisherfolk who live off fishing in the river Titash. The novel is about three generations of the Mallas, about their recurring tragedies and the story of Ananta, a child born of parents who were tragically separated after their wedding night. Ananta leaves the community to get educated in the city. The novel describes the community life of the Mallas in great detail, their Holi and Kali Puja festivals, boat races, bhatiali songs, their relationships of friendship and animosity with the peasants and the oppression of the upper castes. Slowly the community breaks up and the Mallas start fighting amongst themselves as new cultural influences from the city start penetrating their lives. The life of the community and that of the river is intimately tied. Their end comes together as the river dries up, the community dies too. While novelists before Burman had featured low castes as their protagonists, Titash is special because the author is himself from a low-caste, fisherfolk community. Over time, the medium of the novel made room for the experiences of communities that had not received much space in the literary scene earlier. Vaikkom Muhammad Basheer (1908-94), for example, was one of the early Muslim writers to gain wide renown as a novelist in Malayalam. Basheer had little formal education. Most of his works were based on his own rich personal experience rather than on books from the past. When he was in class five at school, Basheer left home to take part in the Salt Satyagraha. Later he spent years wandering in different parts of India and travelling even to Arabia, working in a ship, living with Sufis and Hindu sanyasis, and training as a wrestler. Basheers short novels and stories were written in the ordinary language of conversation. With wonderful humour, Basheers novels spoke about details from the everyday life of Muslim households. He also brought into Malayalam writing themes which were considered very unusual at that time poverty, insanity and life in prisons. Fig. 23 Basheer carrying books. In his early years as a writer, Basheer had great difficulty earning a living from his books. He often sold them himself, carrying copies personally to houses and shops. 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STATISTICS 269 Example 3 The distribution below shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean number of wickets by choosing a suitable method. What does the mean signify? Number of 20 - 60 60 - 100 100 - 150 150 - 250 250 - 350 350 - 450 wickets Number of 7 5 16 12 2 3 bowlers Solution Here, the class size varies, and the xi ,s are large. Let us still apply the step- deviation method with a 200 and h 20. Then, we obtain the data as in Table 14.8. Table 14.8 Number of Number of xi di xi 200 20 i i d u ui fi wickets bowlers taken ( fi) 20 - 60 7 40 160 8 56 60 - 100 5 80 120 6 30 100 - 150 16 125 75 3.75 60 150 - 250 12 200 0 0 0 250 - 350 2 300 100 5 10 350 - 450 3 400 200 10 30 Total 45 106 So, 106 45 u Therefore, x 200 106 20 45 200 47.11 152.89. This tells us that, on an average, the number of wickets taken by these 45 bowlers in one-day cricket is 152.89. 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106 MATHEMATICS Theorem 6.8 If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles. It is obvious from the above theorem that an exterior angle of a triangle is greater than either of its interior apposite angles. Now, let us take some examples based on the above theorems. Example 7 In Fig. 6.37, if QT PR, TQR 40 and SPR 30, find x and y. Solution In TQR, 90 40 x 180 (Angle sum property of a triangle) Therefore, x 50 Now, y SPR x (Theorem 6.8) Therefore, y 30 50 80 Example 8 In Fig. 6.38, the sides AB and AC of ABC are produced to points E and D respectively. If bisectors BO and CO of CBE and BCD respectively meet at point O, then prove that BOC 90 1 2 BAC. Solution Ray BO is the bisector of CBE. Therefore, CBO 1 2 CBE 1 2 (180 y) 90 2 y (1) Similarly, ray CO is the bisector of BCD. 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8 MATHEMATICS In the same way, you can locate n for any positive integer n, after 1 n has been located. EXERCISE 1.2 1. State whether the following statements are true or false. Justify your answers. (i) Every irrational number is a real number. (ii) Every point on the number line is of the form m , where m is a natural number. (iii) Every real number is an irrational number. 2. Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number. 3. Show how 5 can be represented on the number line. 4. Classroom activity (Constructing the square root spiral) Take a large sheet of paper and construct the square root spiral in the following fashion. Start with a point O and draw a line segment OP1 of unit length. Draw a line segment P1P2 perpendicular to OP1 of unit length (see Fig. 1.9). Now draw a line segment P2P3 perpendicular to OP2. Then draw a line segment P3P4 perpendicular to OP3. Continuing in this manner, you can get the line segment Pn1Pn by drawing a line segment of unit length perpendicular to OPn1. In this manner, you will have created the points P2, P3,...., Pn,... ., and joined them to create a beautiful spiral depicting 2, 3, 4, ... 1.3 Real Numbers and their Decimal Expansions In this section, we are going to study rational and irrational numbers from a different point of view. We will look at the decimal expansions of real numbers and see if we can use the expansions to distinguish between rationals and irrationals. We will also explain how to visualise the representation of real numbers on the number line using their decimal expansions. Since rationals are more familiar to us, let us start with them. Let us take three examples 10 7 1 , , 3 8 7 . Pay special attention to the remainders and see if you can find any pattern. 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195 Novels, Society and History It is not surprising that many men were suspicious of women writing novels or reading them. This suspicion cut across communities. Hannah Mullens, a Christian missionary and the author of Karuna o Phulmonir Bibaran (1852), reputedly the first novel in Bengali, tells her readers that she wrote in secret. In the twentieth century, Sailabala Ghosh Jaya, a popular novelist, could only write because her husband protected her. As we have seen in the case of the south, women and girls were often discouraged from reading novels. 4.1 Caste Practices, Lower-Castes and Minorities As you have seen, Indulekha was a love story. But it was also about an issue that was hotly debated at the time when the novel was written. This concerned the marriage practices of upper-caste Hindus in Kerala, especially the Nambuthiri Brahmins and the Nayars. Nambuthiris were also major landlords in Kerala at that time and a large section of the Nayars were their tenants. In late-nineteenth- century Kerala, a younger generation of English-educated Nayar men who had acquired property and wealth on their own, began arguing strongly against Nambuthiri alliances with Nayar women. They wanted new laws regarding marriage and property. The story of Indulekha is interesting in the light of these debates. Suri Nambuthiri, the foolish landlord who comes to marry Indulekha, is the focus of much satire in the novel. The intelligent heroine rejects him and chooses Madhavan, the educated and handsome Nayar as her husband, and the young couple move to Madras, where Madhavan joins the civil service. Suri Nambuthiri, desperate to find a partner for himself, finally marries a poorer relation from the same family and goes away pretending that he has married Indulekha! Chandu Menon clearly wanted his readers to appreciate the new values of his hero and heroine and criticise the ignorance and immorality of Suri Nambuthiri. Novels like Indirabai and Indulekha were written by members of the upper castes, and were primarily about upper-caste characters. But not all novels were of this kind. Potheri Kunjambu, a lower-caste writer from north Kerala, wrote a novel called Saraswativijayam in 1892, mounting a strong attack on caste oppression. This novel shows a young man from an untouchable caste, leaving his village to escape the cruelty of his Brahmin landlord. He converts to Christianity, obtains modern Women with books These days we can see women in black bordered sarees with massive books in their hands, walking inside their houses. Often seeing them with these books in hand, their brothers or husbands are seized with fear in case they are asked for meanings. Sadharani, 1880. Box 8 Fig. 22 Malabar Beauty, painting by Ravi Varma. Chandu Menon thought that the novel was similar to new trends in Indian painting. One of the foremost oil painters of this time was Raja Ravi Varma (1848- 1906). 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Acids, Bases and Salts What is the pH of the soil in your backyard? Plants require a specific pH range for their healthy growth. To find out the pH required for the healthy growth of a plant, you can collect the soil from various places and check the pH in the manner described below in Activity 2.12. Also, you can note down which plants are growing in the region from which you have collected the soil. Acids in other planets The atmosphere of venus is made up of thick white and yellowish clouds of sulphuric acid. Do you think life can exist on this planet? Put about 2 g soil in a test tube and add 5 mL water to it. Shake the contents of the test tube. Filter the contents and collect the filtrate in a test tube. Check the pH of this filtrate with the help of universal indicator paper. What can you conclude about the ideal soil pH for the growth of plants in your region? pH in our digestive system It is very interesting to note that our stomach produces hydrochloric acid. It helps in the digestion of food without harming the stomach. During indigestion the stomach produces too much acid and this causes pain and irritation. To get rid of this pain, people use bases called antacids. One such remedy must have been suggested by you at the beginning of this Chapter. These antacids neutralise the excess acid. Magnesium hydroxide (Milk of magnesia), a mild base, is often used for this purpose. pH change as the cause of tooth decay Tooth decay starts when the pH of the mouth is lower than 5.5. Tooth enamel, made up of calcium hydroxyapatite (a crystalline form of calcium phosphate) is the hardest substance in the body. It does not dissolve in water, but is corroded when the pH in the mouth is below 5.5. Bacteria present in the mouth produce acids by degradation of sugar and food particles remaining in the mouth after eating. The best way to prevent this is to clean the mouth after eating food. Using toothpastes, which are generally basic, for cleaning the teeth can neutralise the excess acid and prevent tooth decay. Self defence by animals and plants through chemical warfare Have you ever been stung by a honey-bee? Bee-sting leaves an acid which causes pain and irritation. Use of a mild base like baking soda on the stung area gives relief. 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TRIANGLES 139 Fig. 6.34 2. In Fig. 6.35, ODC OBA, BOC 125 and CDO 70. Find DOC, DCO and OAB. 3. Diagonals AC and BD of a trapezium ABCD with AB DC intersect each other at the point O. 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316 MATHEMATICS Now, we also have to find the number of years by which the enrolment will reach 50. So, we have to find the value of n in the equation or formula 50 41.9 0.22n (2) Step 2 Solution Solving (2) for n, we get n 50 41.9 8.1 36.8 0.22 0.22 Step 3 Interpretation Since the number of years is an integral value, we will take the next higher integer, 37. So, the enrolment percentage will reach 50 in 1991 37 2028. In a word problem, we generally stop here. But, since we are dealing with a real- life situation, we have to see to what extent this value matches the real situation. Step 4 Validation Let us check if Formula (2) is in agreement with the reality. Let us find the values for the years we already know, using Formula (2), and compare it with the known values by finding the difference. The values are given in Table A2.4. Table A2.4 Year Enrolment Values given by (2) Difference (in ) (in ) (in ) 0 41.9 41.90 0 1 42.6 42.12 0.48 2 42.7 42.34 0.36 3 42.9 42.56 0.34 4 43.1 42.78 0.32 5 43.2 43.00 0.20 6 43.5 43.22 0.28 7 43.5 43.44 0.06 8 43.6 43.66 0.06 9 43.7 43.88 0.18 10 44.1 44.10 0.00 As you can see, some of the values given by Formula (2) are less than the actual values by about 0.3 or even by 0.5. This can give rise to a difference of about 3 to 5 years since the increase per year is actually 1 to 2. 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25 Nationalism in Europe Fig. 19 Germania guarding the Rhine. In 1860, the artist Lorenz Clasen was commissioned to paint this image. The inscription on Germanias sword reads The German sword protects the German Rhine. Look once more at Fig. 10. Imagine you were a citizen of Frankfurt in March 1848 and were present during the proceedings of the parliament. How would you (a) as a man seated in the hall of deputies, and (b) as a woman observing from the galleries, relate to the banner of Germania hanging from the ceiling? 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Forest Society and Colonialism 75 In Section II we will shift our focus to the study of livelihoods and economies. We will look at how the lives of forest dwellers and pastoralists changed in the modern world and how they played a part in shaping these changes. All too often in looking at the emergence of the modern world, we only focus on factories and cities, on the industrial and agricultural sectors which supply the market. But we forget that there are other economies outside these sectors, other people too who matter to the nation. To modern eyes, the lives of pastoralists and forest dwellers, the shifting cultivators and food gatherers often seem to be stuck in the past. It is as if their lives are not important when we study the emergence of the contemporary world. The chapters in Section II will suggest that we need to know about their lives, see how they organise their world and operate their economies. These communities are very much part of the modern world we live in today. They are not simply survivors from a bygone era. Chapter IV will take you into the forest and tell you about the variety of ways the forests were used by communities living within them. It will show how in the nineteenth century the growth of industries and urban centres, ships and railways, created a new demand on the forests for timber and other forest products. New demands led to new rules of forest use, new ways of organising the forest. You will see how colonial control was established over the forests, how forest areas were mapped, trees were classified, and plantations were developed. All these developments affected the lives of those local communities who used forest resources. They were forced to operate within new systems and reorganise their lives. But they also rebelled against the rules and persuaded the state to change its policies. The chapter will give you an idea of the history of such developments in India and Indonesia. SECTION II LIVELIHOODS, ECONOMIES AND SOCIETIES LIVELIHOODS, ECONOMIES AND SOCIETIES 2019-2020	[ 49578, 13278, 323, 72748, 2142, 220, 22, 20, 758, 11113, 7946, 582, 686, 6407, 1039, 5244, 311, 279, 3920, 315, 63651, 82, 323, 36571, 13, 1205, 686, 1401, 518, 1246, 279, 6305, 315, 13638, 43835, 388, 323, 89271, 1671, 5497, 304, 279, 6481, 1879, 323, 1246, 807, 6342, 264, 949, 304, 45520, 1493, 4344, 13, 2009, 2238, 3545, 304, 3330, 518, 279, 48079, 315, 279, 6481, 1879, 11, 582, 1172, 5244, 389, 34059, 323, 9720, 11, 389, 279, 12785, 323, 28049, 25512, 892, 8149, 279, 3081, 13, 1988, 582, 10667, 429, 1052, 525, 1008, 36571, 4889, 1493, 25512, 11, 1008, 1251, 2238, 879, 4925, 311, 279, 6995, 13, 2014, 6481, 6414, 11, 279, 6305, 315, 89271, 1671, 323, 13638, 43835, 388, 11, 279, 31831, 26883, 2973, 323, 3607, 9567, 388, 3545, 2803, 311, 387, 15700, 304, 279, 3267, 13, 1084, 374, 438, 421, 862, 6305, 525, 537, 2989, 979, 582, 3920, 279, 48079, 315, 279, 18706, 1879, 13, 576, 29632, 304, 11113, 7946, 686, 4190, 429, 582, 1184, 311, 1414, 911, 862, 6305, 11, 1490, 1246, 807, 69940, 862, 1879, 323, 14476, 862, 36571, 13, 4220, 10744, 525, 1602, 1753, 949, 315, 279, 6481, 1879, 582, 3887, 304, 3351, 13, 2379, 525, 537, 4936, 31596, 504, 264, 553, 45596, 11385, 13, 15585, 16824, 686, 1896, 498, 1119, 279, 13638, 323, 3291, 498, 911, 279, 8045, 315, 5510, 279, 35558, 1033, 1483, 553, 10744, 5382, 2878, 1105, 13, 1084, 686, 1473, 1246, 304, 279, 64989, 9294, 279, 6513, 315, 19102, 323, 15662, 35182, 11, 17727, 323, 95147, 11, 3465, 264, 501, 7479, 389, 279, 35558, 369, 44788, 323, 1008, 13638, 3871, 13, 1532, 18154, 6069, 311, 501, 5601, 315, 13638, 990, 11, 501, 5510, 315, 87071, 279, 13638, 13, 1446, 686, 1490, 1246, 36583, 2524, 572, 9555, 916, 279, 35558, 11, 1246, 13638, 5671, 1033, 23844, 11, 12408, 1033, 21091, 11, 323, 6008, 804, 1033, 7881, 13, 2009, 1493, 24961, 11495, 279, 6305, 315, 1846, 2205, 10744, 879, 1483, 13638, 4963, 13, 2379, 1033, 9575, 311, 14476, 2878, 501, 5942, 323, 312, 8462, 1064, 862, 6305, 13, 1988, 807, 1083, 35317, 832, 2348, 279, 5601, 323, 64001, 279, 1584, 311, 2297, 1181, 10186, 13, 576, 12453, 686, 2968, 498, 458, 4522, 315, 279, 3840, 315, 1741, 24961, 304, 6747, 323, 23968, 13, 42333, 7946, 444, 3090, 2749, 40, 23818, 2069, 50, 11, 468, 5790, 1898, 5369, 3567, 5627, 11237, 1348, 5369, 444, 3090, 2749, 40, 23818, 2069, 50, 11, 468, 5790, 1898, 5369, 3567, 5627, 11237, 1348, 5369, 220, 17, 15, 16, 24, 12, 17, 15, 17, 15, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645 ]	[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
Pastoralists in the Modern World 101 Activity Source B In Karnataka and Andhra Pradesh, again, the dry central plateau was covered with stone and grass, inhabited by cattle, goat and sheep herders. The Gollas herded cattle. The Kurumas and Kurubas reared sheep and goats and sold woven blankets. They lived near the woods, cultivated small patches of land, engaged in a variety of petty trades and took care of their herds. Unlike the mountain pastoralists, it was not the cold and the snow that defined the seasonal rhythms of their movement rather it was the alternation of the monsoon and dry season. In the dry season they moved to the coastal tracts, and left when the rains came. Only buffaloes liked the swampy, wet conditions of the coastal areas during the monsoon months. Other herds had to be shifted to the dry plateau at this time. Banjaras were yet another well-known group of graziers. They were to be found in the villages of Uttar Pradesh, Punjab, Rajasthan, Madhya Pradesh and Maharashtra. In search of good pastureland for their cattle, they moved over long distances, selling plough cattle and other goods to villagers in exchange for grain and fodder. The accounts of many travellers tell us about the life of pastoral groups. In the early nineteenth century, Buchanan visited the Gollas during his travel through Mysore. He wrote Their families live in small villages near the skirt of the woods, where they cultivate a little ground, and keep some of their cattle, selling in the towns the produce of the dairy. Their families are very numerous, seven to eight young men in each being common. Two or three of these attend the flocks in the woods, while the remainder cultivate their fields, and supply the towns with firewood, and with straw for thatch. From Francis Hamilton Buchanan, A Journey from Madras through the Countries of Mysore, Canara and Malabar (London, 1807). Read Sources A and B. Write briefly about what they tell you about the nature of the work undertaken by men and women in pastoral households. Why do you think pastoral groups often live on the edges of forests? In the deserts of Rajasthan lived the Raikas. The rainfall in the region was meagre and uncertain. On cultivated land, harvests fluctuated every year. Over vast stretches no crop could be grown. So the Raikas combined cultivation with pastoralism. During the monsoons, the Raikas of Barmer, Jaisalmer, Jodhpur and Bikaner stayed in their home villages, where pasture was available. By October, when these grazing grounds were dry and exhausted, they moved out in search of other pasture and water, and returned again during the next monsoon. One group of Raikas known as the Maru (desert) Raikas herded camels and another group reared sheep and goat. Fig.6 A camel herder in his settlement. This is on the Thar desert near Jaisalmer in Rajasthan. 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The organised sector offers jobs that are the most sought-after. But the employment opportunities in the organised sector have been expanding very slowly. It is also common to find many organised sector enterprises in the unorganised sector. They adopt such strategies to evade taxes and refuse to follow laws that protect labourers. As a result, a large number of workers are forced to enter the unorganised sector jobs, which pay a very low salary. They are often exploited and not paid a fair wage. Their earnings are low and not regular. These jobs are not secure and have no other benefits. Since the 1990s, it is also common to see a large number of workers losing their jobs in the organised sector. These workers are forced to take up jobs in the unorganised sector with low earnings. Hence, besides the need for more work, there is also a need for protection and support of the workers in the unorganised sector. Who are these vulnerable people who need protection? In the rural areas, the unorganised sector mostly comprises of landless agricultural labourers, small and marginal farmers, sharecroppers and artisans (such as weavers, blacksmiths, carpenters and goldsmiths). Nearly 80 per cent of rural households in India are in small and marginal farmer category. These farmers need to be supported through adequate facility for timely delivery of seeds, agricultural inputs, credit, storage facilities and marketing outlets. In the urban areas, unorganised sector comprises mainly of workers in small-scale industry, casual workers in construction, trade and transport etc., and those who work as street vendors, head load workers, garment makers, rag pickers etc. Small-scale industry also needs governments support for procuring raw material and marketing of output. The casual workers in both rural and urban areas need to be protected. We also find that majority of workers from scheduled castes, tribes and backward communities find themselves in the unorganised sector. Besides getting the irregular and low paid work, these workers also face social discrimination. Protection and support to the unorganised sector workers is thus necessary for both economic and social development. 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168 MATHEMATICS CHAPTER 10 CIRCLES 10.1 Introduction You may have come across many objects in daily life, which are round in shape, such as wheels of a vehicle, bangles, dials of many clocks, coins of denominations 50 p, Re 1 and Rs 5, key rings, buttons of shirts, etc. (see Fig.10.1). In a clock, you might have observed that the seconds hand goes round the dial of the clock rapidly and its tip moves in a round path. This path traced by the tip of the seconds hand is called a circle. In this chapter, you will study about circles, other related terms and some properties of a circle. 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Life Processes design in multi-cellular organisms are followed, a specialised tissue for excretion will be developed, which means that the transportation system will need to transport waste away from cells to this excretory tissue. Let us consider these various processes, so essential to maintain life, one by one. 1. Why is diffusion insufficient to meet the oxygen requirements of multi- cellular organisms like humans? 2. What criteria do we use to decide whether something is alive? 3. What are outside raw materials used for by an organism? 4. What processes would you consider essential for maintaining life? When we walk or ride a bicycle, we are using up energy. Even when we are not doing any apparent activity, energy is needed to maintain a state of order in our body. We also need materials from outside in order to grow, develop, synthesise protein and other substances needed in the body. This source of energy and materials is the food we eat. How do living things get their food? The general requirement for energy and materials is common in all organisms, but it is fulfilled in different ways. Some organisms use simple food material obtained from inorganic sources in the form of carbon dioxide and water. These organisms, the autotrophs, include green plants and some bacteria. Other organisms utilise complex substances. These complex substances have to be broken down into simpler ones before they can be used for the upkeep and growth of the body. To achieve this, organisms use bio-catalysts called enzymes. Thus, the heterotrophs survival depends directly or indirectly on autotrophs. Heterotrophic organisms include animals and fungi. Carbon and energy requirements of the autotrophic organism are fulfilled by photosynthesis. It is the process by which autotrophs take in substances from the outside and convert them into stored forms of energy. This material is taken in the form of carbon dioxide and water which is converted into carbohydrates in the presence of sunlight and chlorophyll. Carbohydrates are utilised for providing energy to the plant. We will study how this takes place in the next section. The carbohydrates which are not used immediately are stored in the form of starch, which serves as the internal energy reserve to be used as and when required by the plant. A somewhat similar situation is seen in us where some of the energy derived from the food we eat is stored in our body in the form of glycogen. 2019-20	[ 25749, 62303, 2884, 304, 7299, 31901, 1276, 43204, 525, 8110, 11, 264, 87904, 19847, 369, 505, 88690, 686, 387, 7881, 11, 892, 3363, 429, 279, 17903, 1849, 686, 1184, 311, 7557, 12291, 3123, 504, 7761, 311, 419, 505, 4423, 679, 19847, 13, 6771, 601, 2908, 1493, 5257, 11364, 11, 773, 7565, 311, 10306, 2272, 11, 825, 553, 825, 13, 220, 16, 13, 8429, 374, 57330, 38313, 311, 3367, 279, 23552, 8502, 315, 7299, 12, 34593, 43204, 1075, 12677, 30, 220, 17, 13, 3555, 12890, 653, 582, 990, 311, 10279, 3425, 2494, 374, 13675, 30, 220, 18, 13, 3555, 525, 4889, 7112, 7236, 1483, 369, 553, 458, 46020, 30, 220, 19, 13, 3555, 11364, 1035, 498, 2908, 7565, 369, 20337, 2272, 30, 3197, 582, 4227, 476, 11877, 264, 34986, 11, 582, 525, 1667, 705, 4802, 13, 7418, 979, 582, 525, 537, 3730, 894, 9981, 5702, 11, 4802, 374, 4362, 311, 10306, 264, 1584, 315, 1973, 304, 1039, 2487, 13, 1205, 1083, 1184, 7236, 504, 4889, 304, 1973, 311, 3063, 11, 2225, 11, 51289, 1064, 12833, 323, 1008, 32055, 4362, 304, 279, 2487, 13, 1096, 2530, 315, 4802, 323, 7236, 374, 279, 3607, 582, 8180, 13, 2585, 653, 5382, 2513, 633, 862, 3607, 30, 576, 4586, 16287, 369, 4802, 323, 7236, 374, 4185, 304, 678, 43204, 11, 714, 432, 374, 40734, 304, 2155, 5510, 13, 4329, 43204, 990, 4285, 3607, 3684, 12180, 504, 304, 60594, 8173, 304, 279, 1352, 315, 12499, 39489, 323, 3015, 13, 4220, 43204, 11, 279, 3078, 354, 21990, 82, 11, 2924, 6176, 10779, 323, 1045, 23157, 13, 6944, 43204, 68052, 6351, 32055, 13, 4220, 6351, 32055, 614, 311, 387, 10865, 1495, 1119, 34288, 6174, 1573, 807, 646, 387, 1483, 369, 279, 96096, 323, 6513, 315, 279, 2487, 13, 2014, 11075, 419, 11, 43204, 990, 16905, 1786, 4212, 98235, 2598, 54967, 13, 14301, 11, 279, 29448, 354, 21990, 82, 19661, 13798, 5961, 476, 45245, 389, 3078, 354, 21990, 82, 13, 472, 1404, 354, 41710, 43204, 2924, 9898, 323, 80440, 13, 21487, 323, 4802, 8502, 315, 279, 3078, 354, 41710, 46020, 525, 40734, 553, 7249, 73667, 13, 1084, 374, 279, 1882, 553, 892, 3078, 354, 21990, 82, 1896, 304, 32055, 504, 279, 4889, 323, 5508, 1105, 1119, 9768, 7586, 315, 4802, 13, 1096, 3684, 374, 4429, 304, 279, 1352, 315, 12499, 39489, 323, 3015, 892, 374, 16099, 1119, 61245, 304, 279, 9362, 315, 39020, 323, 36733, 5127, 24705, 13, 3261, 33558, 973, 525, 4094, 4056, 369, 8241, 4802, 311, 279, 6008, 13, 1205, 686, 3920, 1246, 419, 4990, 1992, 304, 279, 1790, 3772, 13, 576, 61245, 892, 525, 537, 1483, 7069, 525, 9768, 304, 279, 1352, 315, 69081, 11, 892, 17045, 438, 279, 5306, 4802, 20499, 311, 387, 1483, 438, 323, 979, 2567, 553, 279, 6008, 13, 362, 14400, 4428, 6534, 374, 3884, 304, 601, 1380, 1045, 315, 279, 4802, 14257, 504, 279, 3607, 582, 8180, 374, 9768, 304, 1039, 2487, 304, 279, 1352, 315, 71057, 11706, 13, 220, 17, 15, 16, 24, 12, 17, 15, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645 ]	[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
Carbon and its Compounds Ethanoic acid is commonly called acetic acid and belongs to a group of acids called carboxylic acids. 5-8 solution of acetic acid in water is called vinegar and is used widely as a preservative in pickles. The melting point of pure ethanoic acid is 290 K and hence it often freezes during winter in cold climates. This gave rise to its name glacial acetic acid. The group of organic compounds called carboxylic acids are obviously characterised by their acidic nature. However, unlike mineral acids like HCl, which are completely ionised, carboxylic acids are weak acids. Compare the pH of dilute acetic acid and dilute hydrochloric acid using both litmus paper and universal indicator. Are both acids indicated by the litmus test? Does the universal indicator show them as equally strong acids? Take 1 mL ethanol (absolute alcohol) and 1 mL glacial acetic acid along with a few drops of concentrated sulphuric acid in a test tube. Warm in a water-bath for at least five minutes as shown in Fig. 4.11. Pour into a beaker containing 20-50 mL of water and smell the resulting mixture. Reactions of ethanoic acid (i) Esterification reaction Esters are most commonly formed by reaction of an acid and an alcohol. Ethanoic acid reacts with absolute ethanol in the presence of an acid catalyst to give an ester CH COOH CH CH OH CH C C CH CH H O 3 3 2 3 2 3 2 Acid O (E 11 thanoic acid) (Ethanol) (Ester) Generally, esters are sweet-smelling substances. These are used in making perfumes and as flavouring agents. On treating with sodium hydroxide, which is an alkali, the ester is converted back to alcohol and sodium salt of carboxylic acid. This reaction is known as saponification because it is used in the preparation of soap. Soaps are sodium or potassium salts of long chain carboxylic acid. Figure 4.11 Figure 4.11 Figure 4.11 Figure 4.11 Figure 4.11 Formation of ester Alcohol as a fuel Sugarcane plants are one of the most efficient convertors of sunlight into chemical energy. Sugarcane juice can be used to prepare molasses which is fermented to give alcohol (ethanol). Some countries now use alcohol as an additive in petrol since it is a cleaner fuel which gives rise to only carbon dioxide and water on burning in sufficient air (oxygen). 2019-20	[ 36607, 323, 1181, 13317, 3095, 14356, 5652, 292, 13621, 374, 16626, 2598, 1613, 5298, 13621, 323, 17180, 311, 264, 1874, 315, 32869, 2598, 1803, 2011, 88, 415, 32869, 13, 220, 20, 12, 23, 6291, 315, 1613, 5298, 13621, 304, 3015, 374, 2598, 46105, 323, 374, 1483, 13570, 438, 264, 1652, 53168, 304, 3735, 642, 13, 576, 49584, 1459, 315, 10526, 8372, 5652, 292, 13621, 374, 220, 17, 24, 15, 730, 323, 16085, 432, 3545, 93377, 2337, 12406, 304, 9255, 91299, 13, 1096, 6551, 10000, 311, 1181, 829, 2770, 32111, 1613, 5298, 13621, 13, 576, 1874, 315, 17356, 31146, 2598, 1803, 2011, 88, 415, 32869, 525, 13900, 3668, 4056, 553, 862, 83803, 6993, 13, 4354, 11, 19836, 24136, 32869, 1075, 472, 5066, 11, 892, 525, 6587, 27672, 4056, 11, 1803, 2011, 88, 415, 32869, 525, 7469, 32869, 13, 23768, 279, 36043, 315, 18840, 1070, 1613, 5298, 13621, 323, 18840, 1070, 16643, 71867, 292, 13621, 1667, 2176, 13020, 37727, 5567, 323, 20178, 20438, 13, 8713, 2176, 32869, 16317, 553, 279, 13020, 37727, 1273, 30, 12553, 279, 20178, 20438, 1473, 1105, 438, 18308, 3746, 32869, 30, 11778, 220, 16, 64070, 61672, 320, 17182, 12904, 8, 323, 220, 16, 64070, 2770, 32111, 1613, 5298, 13621, 3156, 448, 264, 2421, 21025, 315, 37526, 82678, 324, 292, 13621, 304, 264, 1273, 13705, 13, 45763, 304, 264, 3015, 1455, 587, 369, 518, 3245, 4236, 4420, 438, 6839, 304, 23095, 13, 220, 19, 13, 16, 16, 13, 25968, 1119, 264, 387, 4407, 8482, 220, 17, 15, 12, 20, 15, 64070, 315, 3015, 323, 22068, 279, 12942, 20980, 13, 1032, 4020, 315, 8372, 5652, 292, 13621, 320, 72, 8, 468, 3667, 2404, 12720, 9403, 388, 525, 1429, 16626, 14122, 553, 12720, 315, 458, 13621, 323, 458, 12904, 13, 14356, 5652, 292, 13621, 68845, 448, 10740, 61672, 304, 279, 9362, 315, 458, 13621, 50383, 311, 2968, 458, 1788, 261, 6826, 7284, 46761, 6826, 6826, 28722, 6826, 356, 356, 6826, 6826, 472, 506, 220, 18, 220, 18, 220, 17, 220, 18, 220, 17, 220, 18, 220, 17, 49134, 506, 320, 36, 220, 16, 16, 1091, 78, 292, 13621, 8, 320, 65390, 38610, 8, 320, 36, 3667, 8, 43393, 11, 1788, 388, 525, 10226, 4668, 6293, 32055, 13, 4220, 525, 1483, 304, 3259, 21784, 18618, 323, 438, 46597, 287, 13009, 13, 1913, 26625, 448, 38595, 16643, 87, 577, 11, 892, 374, 458, 57898, 7956, 11, 279, 1788, 261, 374, 16099, 1182, 311, 12904, 323, 38595, 12021, 315, 1803, 2011, 88, 415, 13621, 13, 1096, 12720, 374, 3881, 438, 274, 10736, 2404, 1576, 432, 374, 1483, 304, 279, 17975, 315, 26785, 13, 2055, 2625, 525, 38595, 476, 61175, 77135, 315, 1293, 8781, 1803, 2011, 88, 415, 13621, 13, 19037, 220, 19, 13, 16, 16, 19037, 220, 19, 13, 16, 16, 19037, 220, 19, 13, 16, 16, 19037, 220, 19, 13, 16, 16, 19037, 220, 19, 13, 16, 16, 71366, 315, 1788, 261, 44296, 438, 264, 10416, 83767, 8198, 2145, 10779, 525, 825, 315, 279, 1429, 11050, 5508, 1087, 315, 39020, 1119, 11483, 4802, 13, 83767, 8198, 2145, 22815, 646, 387, 1483, 311, 10549, 21609, 50990 ]	[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
PROOFS IN MATHEMATICS 293 2. Once again you are given four cards. Each card has a number printed on one side and a letter on the other side. Which are the only two cards you need to turn over to check whether the following rule holds? If a card has a consonant on one side, then it has an odd number on the other side. A1.4 Theorems, Conjectures and Axioms So far we have discussed statements and how to check their validity. In this section, you will study how to distinguish between the three different kinds of statements mathematics is built up from, namely, a theorem, a conjecture and an axiom. You have already come across many theorems before. So, what is a theorem? A mathematical statement whose truth has been established (proved) is called a theorem. For example, the following statements are theorems, as you will see in Section A1.5. Theorem A1.1 The sum of the interior angles of a triangle is 180. Theorem A1.2 The product of two even natural numbers is even. Theorem A1.3 The product of any three consecutive even natural numbers is divisible by 16. A conjecture is a statement which we believe is true, based on our mathematical understanding and experience, that is, our mathematical intuition. The conjecture may turn out to be true or false. If we can prove it, then it becomes a theorem. Mathematicians often come up with conjectures by looking for patterns and making intelligent mathematical guesses. Let us look at some patterns and see what kind of intelligent guesses we can make. Example 4 Take any three consecutive even numbers and add them, say, 2 4 6 12, 4 6 8 18, 6 8 10 24, 8 10 12 30, 20 22 24 66. Is there any pattern you can guess in these sums? What can you conjecture about them? Solution One conjecture could be (i) the sum of three consecutive even numbers is even. 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Lincoln to us Democracy is government of the people, by the people and for the people. We in Meghalaya always ruled ourselves. That is accepted by everyone. Why do we need to change that? Lyngdoh Madam I am not saying we need to change it. I too find this definition very beautiful. 2019-20	[ 50597, 22033, 311, 601, 47089, 374, 3033, 315, 279, 1251, 11, 553, 279, 1251, 323, 369, 279, 1251, 13, 1205, 304, 27343, 11866, 12589, 2677, 21286, 13217, 13, 2938, 374, 11666, 553, 5019, 13, 8429, 653, 582, 1184, 311, 2297, 429, 30, 15953, 968, 67, 2267, 9483, 309, 358, 1079, 537, 5488, 582, 1184, 311, 2297, 432, 13, 358, 2238, 1477, 419, 7271, 1602, 6233, 13, 220, 17, 15, 16, 24, 12, 17, 15, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 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India and the Contemporary World 130 Fig. 2 A Strangers Home, The Illustrated London News,1870. Night Refuges and Strangers Homes were opened in winter by charitable societies and local authorities in many towns. The poor flocked to these places in the hope of food, warmth and shelter. Imagine that you are a newspaper reporter writing a piece on the changes you see in London in 1811. What problems are you likely to write about? Who would have gained from the changes? Activity women, many of them recent migrants. A large number of women used their homes to increase family income by taking in lodgers or through such activities as tailoring, washing or matchbox making. However, there was a change once again in the twentieth century. As women got employment in wartime industries and offices, they withdrew from domestic service. Large number of children were pushed into low-paid work, often by their parents. Andrew Mearns, a clergyman who wrote The Bitter Cry of Outcast London in the 1880s, showed why crime was more profitable than labouring in small underpaid factories A child seven years old is easily known to make 10 shillings 6 pence a week from thieving Before he can gain as much as the young thief a boy must make 56 gross of matchboxes a week, or 1,296 a day. It was only after the passage of the Compulsory Elementary Education Act in 1870, and the factory acts beginning from 1902, that children were kept out of industrial work. 1.3 Housing Older cities like London changed dramatically when people began pouring in after the Industrial Revolution. 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Nazism and the Rise of Hitler 49 In the spring of 1945, a little eleven-year-old German boy called Helmuth was lying in bed when he overheard his parents discussing something in serious tones. His father, a prominent physician, deliberated with his wife whether the time had come to kill the entire family, or if he should commit suicide alone. His father spoke about his fear of revenge, saying, Now the Allies will do to us what we did to the crippled and Jews. The next day, he took Helmuth to the woods, where they spent their last happy time together, singing old childrens songs. Later, Helmuths father shot himself in his office. Helmuth remembers that he saw his fathers bloody uniform being burnt in the family fireplace. So traumatised was he by what he had overheard and what had happened, that he reacted by refusing to eat at home for the following nine years! He was afraid that his mother might poison him. Although Helmuth may not have realised all that it meant, his father had been a Nazi and a supporter of Adolf Hitler. Many of you will know something about the Nazis and Hitler. You probably know of Hitlers determination to make Germany into a mighty power and his ambition of conquering all of Europe. You may have heard that he killed Jews. But Nazism was not one or two isolated acts. It was a system, a structure of ideas about the world and politics. Let us try and understand what Nazism was all about. Let us see why Helmuths father killed himself and what the basis of his fear was. In May 1945, Germany surrendered to the Allies. Anticipating what was coming, Hitler, his propaganda minister Goebbels and his entire family committed suicide collectively in his Berlin bunker in April. At the end of the war, an International Military Tribunal at Nuremberg was set up to prosecute Nazi war criminals for Crimes against Peace, for War Crimes and Crimes Against Humanity. Germanys conduct during the war, especially those actions which Nazism and the Rise Nazism and the Rise Nazism and the Rise Nazism and the Rise Nazism and the Rise of Hitler of Hitler of Hitler of Hitler of Hitler Nazism and the Rise of Hitler Fig.1 Hitler (centre) and Goebbels (left) leaving after an official meeting, 1932. New words Allies The Allied Powers were initially led by the UK and France. In 1941 they were joined by the USSR and USA. They fought against the Axis Powers, namely Germany, Italy and Japan. 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158 MATHEMATICS Let us now take some examples to illustrate the use of the above theorem. Example 1 In Fig. 9.13, ABCD is a parallelogram and EFCD is a rectangle. Also, AL DC. Prove that (i) ar (ABCD) ar (EFCD) (ii) ar (ABCD) DC AL Solution (i) As a rectangle is also a parallelogram, therefore, ar (ABCD) ar (EFCD) (Theorem 9.1) (ii) From above result, ar (ABCD) DC FC (Area of the rectangle length breadth) (1) As AL DC, therefore, AFCL is also a rectangle So, AL FC (2) Therefore, ar (ABCD) DC AL From (1) and (2) Can you see from the Result (ii) above that area of a parallelogram is the product of its any side and the coresponding altitude. Do you remember that you have studied this formula for area of a parallelogram in Class VII. On the basis of this formula, Theorem 9.1 can be rewritten as parallelograms on the same base or equal bases and between the same parallels are equal in area. Can you write the converse of the above statement? It is as follows Parallelograms on the same base (or equal bases) and having equal areas lie between the same parallels. Is the converse true? Prove the converse using the formula for area of the parallelogram. Example 2 If a triangle and a parallelogram are on the same base and between the same parallels, then prove that the area of the triangle is equal to half the area of the parallelogram. Solution Let ABP and parallelogram ABCD be on the same base AB and between the same parallels AB and PC (see Fig. 9.14). You wish to prove that ar (PAB) 1 ar(ABCD) 2 Draw BQ AP to obtain another parallelogram ABQP. Now parallelograms ABQP and ABCD are on the same base AB and between the same parallels AB and PC. 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Gender, Religion and Caste 41 their educational and career opportunities. More radical womens movements aimed at equality in personal and family life as well. These movements are called FEMINIST movements. Political expression of gender division and political mobilisation on this Discuss all these perceptions of an ideal woman that prevail in our society. Do you agree with any of these? If not, what is your image of an ideal woman? Feminist A woman or a man who believes in equal rights and opportunities for women and men. Zuban question helped to improve womens role in public life. We now find women working as scientists, doctors, engineers, lawyers, managers and college and university teachers which were earlier not considered suitable for women. 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150 MATHEMATICS Similarly, from OQD, OD2 OQ2 DQ2 (2) From OQC, we have OC2 OQ2 CQ2 (3) and from OAP, we have OA2 AP2 OP2 (4) Adding (1) and (2), OB2 OD2 BP2 OP2 OQ2 DQ2 CQ2 OP2 OQ2 AP2 (As BP CQ and DQ AP) CQ2 OQ2 OP2 AP2 OC2 OA2 From (3) and (4) EXERCISE 6.5 1. Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse. (i) 7 cm, 24 cm, 25 cm (ii) 3 cm, 8 cm, 6 cm (iii) 50 cm, 80 cm, 100 cm (iv) 13 cm, 12 cm, 5 cm 2. PQR is a triangle right angled at P and M is a point on QR such that PM QR. Show that PM2 QM . MR. 3. In Fig. 6.53, ABD is a triangle right angled at A and AC BD. Show that (i) AB2 BC . BD (ii) AC2 BC . DC (iii) AD2 BD . CD 4. ABC is an isosceles triangle right angled at C. Prove that AB2 2AC2. 5. ABC is an isosceles triangle with AC BC. If AB2 2 AC2, prove that ABC is a right triangle. 6. ABC is an equilateral triangle of side 2a. Find each of its altitudes. 7. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals. 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Poverty as a Challenge 29 Overview This chapter deals with one of the most difficult challenges faced by independent Indiapoverty. After discussing this multi-dimensional problem through examples, the chapter discusses the way poverty is seen in social sciences. Poverty trends in India and the world are illustrated through the concept of the poverty line. Causes of poverty as well as anti-poverty measures taken by the government are also discussed. The chapter ends with broadening the official concept of poverty into human poverty. Introduction In our daily life, we come across many people who we think are poor. They could be landless labourers in villages or people living in overcrowded jhuggis in cities. They could be daily wage workers at construction sites or child workers in Poverty as a Challenge Chapter dhabas. They could also be beggars with children in tatters. We see poverty all around us. In fact, every fourth person in India is poor. This means, roughly 270 million (or 27 crore) people in India live in poverty 2011-12. This also means that India has the largest single concentration of the poor in the world. This illustrates the seriousness of the challenge. Two Typical Cases of Poverty Urban Case Thirty-three year old Ram Saran works as a daily-wage labourer in a wheat flour mill near Ranchi in Jharkhand. He manages to earn around Rs 1,500 a month when he finds employment, which is not often. The money is not enough to sustain his family of six that includes his wife and four children aged between 12 years to six months. 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NATURAL RESOURCES 201 Activity 14.13 Find out which other molecules are thought to damage the ozone layer. Newspaper reports often talk about the hole in the ozone layer. Find out whether the size of this hole is changing and in what manner scientists think this would affect life on Earth (Fig. 14.9). Q What you have learnt Life on Earth depends on resources like soil, water and air, and energy from the Sun. Uneven heating of air over land and water-bodies causes winds. Evaporation of water from water-bodies and subsequent condensation give us rain. Rainfall patterns depend on the prevailing wind patterns in an area. Various nutrients are used again and again in a cyclic fashion. This leads to a certain balance between the various components of the biosphere. Pollution of air, water and soil affect the quality of life and harm the biodiversity. We need to conserve our natural resources and use them in a sustainable manner. Exercises 1. Why is the atmosphere essential for life? 2. Why is water essential for life? 3. How are living organisms dependent on the soil? Are organisms that live in water totally independent of soil as a resource? 4. You have seen weather reports on television and in newspapers. How do you think we are able to predict the weather? uestions 1. What are the different states in which water is found during the water cycle? 2. Name two biologically important compounds that contain both oxygen and nitrogen. 3. List any three human activities which would lead to an increase in the carbon dioxide content of air. 4. What is the greenhouse effect? 5. 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Forest Society and Colonialism 95 4.4 War and Deforestation The First World War and the Second World War had a major impact on forests. In India, working plans were abandoned at this time, and the forest department cut trees freely to meet British war needs. In Java, just before the Japanese occupied the region, the Dutch followed a scorched earth policy, destroying sawmills, and burning huge piles of giant teak logs so that they would not fall into Japanese hands. The Japanese then exploited the forests recklessly for their own war industries, forcing forest villagers to cut down forests. Many villagers used this opportunity to expand cultivation in the forest. After the war, it was difficult for the Indonesian forest service to get this land back. As in India, peoples need for agricultural land has brought them into conflict with the forest departments desire to control the land and exclude people from it. 4.5 New Developments in Forestry Since the 1980s, governments across Asia and Africa have begun to see that scientific forestry and the policy of keeping forest communities away from forests has resulted in many conflicts. Conservation of forests rather than collecting timber has become a more important goal. The government has recognised that in order to meet this goal, the people who live near the forests must be involved. In many cases, across India, from Mizoram to Kerala, dense forests have survived only because villages protected them in sacred groves known as sarnas, devarakudu, kan, rai, etc. Some villages have been patrolling their own forests, with each household taking it in turns, instead of leaving it to the forest guards. Local forest communities and environmentalists today are thinking of different forms of forest management. Fig.23 Indian Munitions Board, War Timber Sleepers piled at Soolay pagoda ready for shipment,1917. The Allies would not have been as successful in the First World War and the Second World War if they had not been able to exploit the resources and people of their colonies. Both the world wars had a devastating effect on the forests of India, Indonesia and elsewhere. The forest department cut freely to satisfy war needs. 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The Story of Village Palampur 7 Lets Discuss In the Picture 1.5, can you shade the land cultivated by the small farmers? Why do so many families of farmers cultivate such small plots of land? The distribution of farmers in India and the amount of land they cultivate is given in the following Graph 1.1. Discuss in the classroom. Graph 1.1 Distribution of Cultivated Area and Farmers Lets Discuss Would you agree that the distribution of cultivated land is unequal in Palampur? Do you find a similar situation for India? Explain. 5. Who will provide the labour? After land, labour is the next necessary factor for production. Farming requires a great deal of hard work. Small farmers along with their families cultivate their own fields. Thus, they provide the labour required for farming themselves. Medium and large farmers hire farm labourers to work on their fields. Lets Discuss Identify the work being done on the field in the Pictures 1.6 and arrange them in a proper sequence. Farm labourers come either from landless families or families cultivating small plots of land. Unlike farmers, farm labourers do not have a right over the Picture 1.6 Work on the fields Wheat crop ploughing by bullocks, sowing, spraying of insecticides, cultivation by traditional method, cultivation by modern method, and cutting of crops. Source Pocket Book of Agriculture Statistics 2017 and State of Indian Agriculture 2017, Department of Agriculture, Cooperation and Farmers Welfare (As per Agriculture Census, 2010 11). 2019-2020	[ 785, 15106, 315, 24069, 10925, 1121, 324, 220, 22, 57066, 65279, 758, 279, 24568, 220, 16, 13, 20, 11, 646, 498, 27501, 279, 4268, 66066, 553, 279, 2613, 20336, 30, 8429, 653, 773, 1657, 8521, 315, 20336, 66532, 1741, 2613, 30694, 315, 4268, 30, 576, 7982, 315, 20336, 304, 6747, 323, 279, 3311, 315, 4268, 807, 66532, 374, 2661, 304, 279, 2701, 12165, 220, 16, 13, 16, 13, 65279, 304, 279, 24017, 13, 12165, 220, 16, 13, 16, 33909, 315, 25594, 54686, 12030, 323, 62322, 57066, 65279, 18885, 498, 7503, 429, 279, 7982, 315, 66066, 4268, 374, 77195, 304, 10925, 1121, 324, 30, 3155, 498, 1477, 264, 4428, 6534, 369, 6747, 30, 81917, 13, 220, 20, 13, 10479, 686, 3410, 279, 22939, 30, 4636, 4268, 11, 22939, 374, 279, 1790, 5871, 8168, 369, 5670, 13, 18438, 287, 7460, 264, 2244, 3484, 315, 2588, 975, 13, 14994, 20336, 3156, 448, 862, 8521, 66532, 862, 1828, 5043, 13, 14301, 11, 807, 3410, 279, 22939, 2567, 369, 32389, 5577, 13, 24355, 323, 3460, 20336, 17983, 8785, 22939, 388, 311, 975, 389, 862, 5043, 13, 57066, 65279, 64547, 279, 975, 1660, 2814, 389, 279, 2070, 304, 279, 28385, 220, 16, 13, 21, 323, 30893, 1105, 304, 264, 6169, 8500, 13, 18438, 22939, 388, 2525, 2987, 504, 4268, 1717, 8521, 476, 8521, 98039, 2613, 30694, 315, 4268, 13, 26048, 20336, 11, 8785, 22939, 388, 653, 537, 614, 264, 1290, 916, 279, 24568, 220, 16, 13, 21, 5547, 389, 279, 5043, 55638, 19097, 625, 1384, 287, 553, 7028, 34936, 11, 274, 23184, 11, 82536, 315, 25989, 75095, 11, 51029, 553, 8606, 1714, 11, 51029, 553, 6481, 1714, 11, 323, 14376, 315, 30565, 13, 8748, 45724, 5893, 315, 36863, 24624, 220, 17, 15, 16, 22, 323, 3234, 315, 7748, 36863, 220, 17, 15, 16, 22, 11, 5887, 315, 36863, 11, 72708, 323, 62322, 65087, 320, 2121, 817, 36863, 45527, 11, 220, 17, 15, 16, 15, 220, 16, 16, 568, 220, 17, 15, 16, 24, 12, 17, 15, 17, 15, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645 ]	[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
250 MATHEMATICS Let us represent the data given above graphically as follows (i) We represent the weights on the horizontal axis on a suitable scale. We can choose the scale as 1 cm 5 kg. Also, since the first class interval is starting from 30.5 and not zero, we show it on the graph by marking a kink or a break on the axis. (ii) We represent the number of students (frequency) on the vertical axis on a suitable scale. Since the maximum frequency is 15, we need to choose the scale to accomodate this maximum frequency. (iii) We now draw rectangles (or rectangular bars) of width equal to the class-size and lengths according to the frequencies of the corresponding class intervals. For example, the rectangle for the class interval 30.5 - 35.5 will be of width 1 cm and length 4.5 cm. (iv) In this way, we obtain the graph as shown in Fig. 14.3 Fig. 14.3 Observe that since there are no gaps in between consecutive rectangles, the resultant graph appears like a solid figure. This is called a histogram, which is a graphical representation of a grouped frequency distribution with continuous classes. Also, unlike a bar graph, the width of the bar plays a significant role in its construction. Here, in fact, areas of the rectangles erected are proportional to the corresponding frequencies. However, since the widths of the rectangles are all equal, the lengths of the rectangles are proportional to the frequencies. 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Magnetic Effects of Electric Current We know that the magnetic field produced by a current-carrying wire at a given point depends directly on the current passing through it. Therefore, if there is a circular coil having n turns, the field produced is n times as large as that produced by a single turn. This is because the current in each circular turn has the same direction, and the field due to each turn then just adds up. Take a rectangular cardboard having two holes. Insert a circular coil having large number of turns through them, normal to the plane of the cardboard. Connect the ends of the coil in series with a battery, a key and a rheostat, as shown in Fig. 13.9. Sprinkle iron filings uniformly on the cardboard. Plug the key. Tap the cardboard gently a few times. Note the pattern of the iron filings that emerges on the cardboard. Figure 13.9 Figure 13.9 Figure 13.9 Figure 13.9 Figure 13.9 Magnetic field produced by a current- carrying circular coil. A coil of many circular turns of insulated copper wire wrapped closely in the shape of a cylinder is called a solenoid. The pattern of the magnetic field lines around a current-carrying solenoid is shown in Fig. 13.10. Compare the pattern of the field with the magnetic field around a bar magnet (Fig. 13.4). Do they look similar? Yes, they are similar. In fact, one end of the solenoid behaves as a magnetic north pole, while the other behaves as the south pole. The field lines inside the solenoid are in the form of parallel straight lines. This indicates that the magnetic field is the same at all points inside the solenoid. That is, the field is uniform inside the solenoid. A strong magnetic field produced inside a solenoid can be used to magnetise a piece of magnetic material, like soft iron, when placed inside the coil (Fig. 13.11). The magnet so formed is called an electromagnet. Figure 13.10 Figure 13.10 Figure 13.10 Figure 13.10 Figure 13.10 Field lines of the magnetic field through and around a current carrying solenoid. Figure 13.11 Figure 13.11 Figure 13.11 Figure 13.11 Figure 13.11 A current-carrying solenoid coil is used to magnetise steel rod inside it an electromagnet. 1. Consider a circular loop of wire lying in the plane of the table. Let the current pass through the loop clockwise. Apply the right-hand rule to find out the direction of the magnetic field inside and outside the loop. 2. The magnetic field in a given region is uniform. 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SCIENCE 62 Was there a darkly coloured, spherical or oval, dot-like structure near the centre of each cell? This structure is called nucleus. Were there similar structures in onion peel cells? The nucleus has a double layered covering called nuclear membrane. The nuclear membrane has pores which allow the transfer of material from inside the nucleus to its outside, that is, to the cytoplasm (which we will talk about in section 5.2.4). The nucleus contains chromosomes, which are visible as rod-shaped structures only when the cell is about to divide. Chromosomes contain information for inheritance of characters from parents to next generation in the form of DNA (Deoxyribo Nucleic Acid) molecules. Chromosomes are composed of DNA and protein. DNA molecules contain the information necessary for constructing and organising cells. Functional segments of DNA are called genes. In a cell which is not dividing, this DNA is present as part of chromatin material. Chromatin material is visible as entangled mass of thread like structures. Whenever the cell is about to divide, the chromatin material gets organised into chromosomes. The nucleus plays a central role in cellular reproduction, the process by which a single cell divides and forms two new cells. It also plays a crucial part, along with the environment, in determining the way the cell will develop and what form it will exhibit at maturity, by directing the chemical activities of the cell. In some organisms like bacteria, the nuclear region of the cell may be poorly defined due to the absence of a nuclear membrane. Such an undefined nuclear region containing only nucleic acids is called a nucleoid. Such organisms, whose cells lack a nuclear membrane, are called prokaryotes (Pro primitive or primary karyote karyon nucleus). Organisms with cells having a nuclear membrane are called eukaryotes. Prokaryotic cells (see Fig. 5.4) also lack most of the other cytoplasmic organelles present in eukaryotic cells. Many of the functions of such organelles are also performed by poorly organised parts of the cytoplasm (see section 5.2.4). The chlorophyll in photosynthetic prokaryotic bacteria is associated with membranous vesicles (bag like structures) but not with plastids as in eukaryotic cells (see section 5.2.5). Ribosomes Plasma membrane Cell wall Nucleoid Fig. 5.4 Prokaryotic cell 5.2.4 CYTOPLASM When we look at the temporary mounts of onion peel as well as human cheek cells, we can see a large region of each cell enclosed by the cell membrane. This region takes up very little stain. It is called the cytoplasm. The cytoplasm is the fluid content inside the plasma membrane. It also contains many specialised cell organelles. Each of these organelles performs a specific function for the cell. Cell organelles are enclosed by membranes. In prokaryotes, beside the absence of a defined nuclear region, the membrane-bound cell organelles are also absent. On the other hand, the eukaryotic cells have nuclear membrane as well as membrane-enclosed organelles. The significance of membranes can be illustrated with the example of viruses. 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PAIR OF LINEAR EQUATIONS IN TWO VARIABLES 61 Then (3)( 74) (5)( 46) x 1 ( 46)(3) ( 74)(2) (2)(5) (3)(3) y i.e., 222 230 x 1 138 148 10 9 y i.e., 8 x 1 10 1 y i.e., 8 x 1 1 and 10 y 1 1 i.e., x 8 and y 10 Hence, the fare from the bus stand in Bangalore to Malleswaram is 8 and the fare to Yeshwanthpur is 10. Verification You can check from the problem that the solution we have got is correct. Example 15 For which values of p does the pair of equations given below has unique solution? 4x py 8 0 2x 2y 2 0 Solution Here a1 4, a2 2, b1 p, b2 2. Now for the given pair to have a unique solution 1 2 a a 1 2 b b i.e., 4 2 2 p i.e., p 4 Therefore, for all values of p, except 4, the given pair of equations will have a unique solution. Example 16 For what values of k will the following pair of linear equations have infinitely many solutions? kx 3y (k 3) 0 12x ky k 0 Solution Here, 1 1 1 2 2 2 3 3 , , 12 a b c k k a b k c k For a pair of linear equations to have infinitely many solutions 1 1 1 2 2 2 a b c a b c 2019-20	[ 82966, 3008, 30851, 934, 468, 5757, 21792, 1964, 46258, 76753, 220, 21, 16, 5005, 320, 18, 2376, 220, 22, 19, 8, 320, 20, 2376, 220, 19, 21, 8, 856, 220, 16, 320, 220, 19, 21, 2376, 18, 8, 320, 220, 22, 19, 2376, 17, 8, 320, 17, 2376, 20, 8, 320, 18, 2376, 18, 8, 379, 600, 1734, 2572, 220, 17, 17, 17, 220, 17, 18, 15, 856, 220, 16, 220, 16, 18, 23, 220, 16, 19, 23, 220, 16, 15, 220, 24, 379, 600, 1734, 2572, 220, 23, 856, 220, 16, 220, 16, 15, 220, 16, 379, 600, 1734, 2572, 220, 23, 856, 220, 16, 220, 16, 323, 220, 16, 15, 379, 220, 16, 220, 16, 600, 1734, 2572, 856, 220, 23, 323, 379, 220, 16, 15, 31040, 11, 279, 20425, 504, 279, 5828, 2498, 304, 58125, 311, 8394, 642, 86, 637, 374, 220, 23, 323, 279, 20425, 311, 809, 4288, 16556, 339, 24998, 374, 220, 16, 15, 13, 55473, 1446, 646, 1779, 504, 279, 3491, 429, 279, 6291, 582, 614, 2684, 374, 4396, 13, 13383, 220, 16, 20, 1752, 892, 2750, 315, 281, 1558, 279, 6716, 315, 37906, 2661, 3685, 702, 4911, 6291, 30, 220, 19, 87, 4510, 220, 23, 220, 15, 220, 17, 87, 220, 17, 88, 220, 17, 220, 15, 12478, 5692, 264, 16, 220, 19, 11, 264, 17, 220, 17, 11, 293, 16, 281, 11, 293, 17, 220, 17, 13, 4695, 369, 279, 2661, 6716, 311, 614, 264, 4911, 6291, 220, 16, 220, 17, 264, 264, 220, 16, 220, 17, 293, 293, 600, 1734, 2572, 220, 19, 220, 17, 220, 17, 281, 600, 1734, 2572, 281, 220, 19, 15277, 11, 369, 678, 2750, 315, 281, 11, 3650, 220, 19, 11, 279, 2661, 6716, 315, 37906, 686, 614, 264, 4911, 6291, 13, 13383, 220, 16, 21, 1752, 1128, 2750, 315, 595, 686, 279, 2701, 6716, 315, 13482, 37906, 614, 71500, 1657, 9904, 30, 595, 87, 220, 18, 88, 320, 74, 220, 18, 8, 220, 15, 220, 16, 17, 87, 54953, 595, 220, 15, 12478, 5692, 11, 220, 16, 220, 16, 220, 16, 220, 17, 220, 17, 220, 17, 220, 18, 220, 18, 1154, 1154, 220, 16, 17, 264, 293, 272, 595, 595, 264, 293, 595, 272, 595, 1752, 264, 6716, 315, 13482, 37906, 311, 614, 71500, 1657, 9904, 220, 16, 220, 16, 220, 16, 220, 17, 220, 17, 220, 17, 264, 293, 272, 264, 293, 272, 220, 17, 15, 16, 24, 12, 17, 15, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645 ]	[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
118 MATHEMATICS Observe that the triangles may or may not be congruent to each other. So, equality of three angles is not sufficient for congruence of triangles. Therefore, for congruence of triangles out of three equal parts, one has to be a side. Let us now take some more examples. Example 3 Line-segment AB is parallel to another line-segment CD. O is the mid-point of AD (see Fig. 7.15). Show that (i) AOB DOC (ii) O is also the mid-point of BC. Solution (i) Consider AOB and DOC. ABO DCO (Alternate angles as AB CD and BC is the transversal) AOB DOC (Vertically opposite angles) OA OD (Given) Therefore, AOB DOC (AAS rule) (ii) OB OC (CPCT) So, O is the mid-point of BC. EXERCISE 7.1 1. In quadrilateral ACBD, AC AD and AB bisects A (see Fig. 7.16). Show that ABC ABD. What can you say about BC and BD? 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India and the Contemporary World 48 In earlier times, foreign travellers in India marvelled at the courage, truthfulness and modesty of the people of the Arya vamsa now they remark mainly on the absence of those qualities. In those days Hindus would set out on conquest and hoist their flags in Tartar, China and other countries now a few soldiers from a tiny island far away are lording it over the land of India. Tarinicharan Chattopadhyay, Bharatbarsher Itihas (The History of Bharatbarsh), vol. 1, 1858. Source E Source revival. In Madras, Natesa Sastri published a massive four-volume collection of Tamil folk tales, The Folklore of Southern India. He believed that folklore was national literature it was the most trustworthy manifestation of peoples real thoughts and characteristics. As the national movement developed, nationalist leaders became more and more aware of such icons and symbols in unifying people and inspiring in them a feeling of nationalism. During the Swadeshi movement in Bengal, a tricolour flag (red, green and yellow) was designed. It had eight lotuses representing eight provinces of British India, and a crescent moon, representing Hindus and Muslims. By 1921, Gandhiji had designed the Swaraj flag. It was again a tricolour (red, green and white) and had a spinning wheel in the centre, representing the Gandhian ideal of self-help. Carrying the flag, holding it aloft, during marches became a symbol of defiance. Another means of creating a feeling of nationalism was through reinterpretation of history. By the end of the nineteenth century many Indians began feeling that to instill a sense of pride in the nation, Indian history had to be thought about differently. The British saw Indians as backward and primitive, incapable of governing themselves. In response, Indians began looking into the past to discover Indias great achievements. They wrote about the glorious developments in ancient times when art and architecture, science and mathematics, religion and culture, law and philosophy, crafts and trade had flourished. This glorious time, in their view, was followed by a history of decline, when India was colonised. These nationalist histories urged the readers to take pride in Indias great achievements in the past and struggle to change the miserable conditions of life under British rule. These efforts to unify people were not without problems. When the past being glorified was Hindu, when the images celebrated were drawn from Hindu iconography, then people of other communities felt left out. Fig. 14a Bharat Mata. This figure of Bharat Mata is a contrast to the one painted by Abanindranath Tagore. Here she is shown with a trishul, standing beside a lion and an elephant both symbols of power and authority. Look at Figs. 12 and 14. Do you think these images will appeal to all castes and communities? Explain your views briefly. 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192 India and the Contemporary World The most popular historical novelist in Tamil was R. Krishnamurthy who wrote under the pen- name Kalki. He was an active participant in the freedom movement and the editor of the widely read Tamil magazines Anandavikatan and Kalki. Written in simple language and full of heroism, adventure and suspense, Kalkis novels captivated the Tamil-reading public of an entire generation. Box 7 Fig. 19 A page from the novel Ponniyin Selvan, written by Kalki and serialised in the magazine Kalki, 1951. world of print for the first time. The way characters spoke in a novel began to indicate their region, class or caste. Thus novels made their readers familiar with the ways in which people in other parts of their land spoke their language. 3.2 The Problem of Being Modern Although they were about imaginary stories, novels often spoke to their readers about the real world. But novels did not always show things exactly as they were in reality. Sometimes, they presented a vision of how things ought to be. Social novelists often created heroes and heroines with ideal qualities, who their readers could admire and imitate. How were these ideal qualities defined? In many novels written during the colonial period, the ideal person successfully deals with one of the central dilemmas faced by colonial subjects how to be modern without rejecting tradition, how to accept ideas coming from the West without losing ones identity. Chandu Menon portrayed Indulekha as a woman of breathtaking beauty, high intellectual abilities, artistic talent, and with an education in English and Sanskrit. Madhavan, the hero of the novel, was also presented in ideal colours. 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228 MATHEMATICS Let us now take some examples to understand these concepts (or results). Example 2 Find the area of the sector of a circle with radius 4 cm and of angle 30. Also, find the area of the corresponding major sector (Use 3.14). Solution Given sector is OAPB (see Fig. 12.8). Area of the sector 2 360 r 2 30 3.14 4 4 cm 360 2 2 12.56 cm 4.19cm 3 (approx.) Area of the corresponding major sector r2 area of sector OAPB (3.14 16 4.19) cm2 46.05 cm2 46.1 cm2(approx.) Alternatively, area of the major sector 2 (360 ) 360 r 2 360 30 3.14 16 cm 360 2 2 330 3.14 16cm 46.05 cm 360 46.1 cm2 (approx.) Example 3 Find the area of the segment AYB shown in Fig. 12.9, if radius of the circle is 21 cm and AOB 120. 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LINEAR EQUATIONS IN TWO VARIABLES 67 While solving an equation, you must always keep the following points in mind The solution of a linear equation is not affected when (i) the same number is added to (or subtracted from) both the sides of the equation. (ii) you multiply or divide both the sides of the equation by the same non-zero number. Let us now consider the following situation In a One-day International Cricket match between India and Sri Lanka played in Nagpur, two Indian batsmen together scored 176 runs. Express this information in the form of an equation. Here, you can see that the score of neither of them is known, i.e., there are two unknown quantities. Let us use x and y to denote them. So, the number of runs scored by one of the batsmen is x, and the number of runs scored by the other is y. We know that x y 176, which is the required equation. This is an example of a linear equation in two variables. It is customary to denote the variables in such equations by x and y, but other letters may also be used. Some examples of linear equations in two variables are 1.2s 3t 5, p 4q 7, u 5v 9 and 3 2 x 7y. Note that you can put these equations in the form 1.2s 3t 5 0, p 4q 7 0, u 5v 9 0 and 2 x 7y 3 0, respectively. So, any equation which can be put in the form ax by c 0, where a, b and c are real numbers, and a and b are not both zero, is called a linear equation in two variables. This means that you can think of many many such equations. Example 1 Write each of the following equations in the form ax by c 0 and indicate the values of a, b and c in each case (i) 2x 3y 4.37 (ii) x 4 3 y (iii) 4 5x 3y (iv) 2x y Solution (i) 2x 3y 4.37 can be written as 2x 3y 4.37 0. Here a 2, b 3 and c 4.37. (ii) The equation x 4 3 y can be written as x 3 y 4 0. Here a 1, b 3 and c 4. (iii) The equation 4 5x 3y can be written as 5x 3y 4 0. Here a 5, b 3 and c 4. Do you agree that it can also be written as 5x 3y 4 0 ? 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India and the Contemporary World 166 5.2 Further Innovations By the late eighteenth century, the press came to be made out of metal. Through the nineteenth century, there were a series of further innovations in printing technology. By the mid-nineteenth century, Richard M. Hoe of New York had perfected the power-driven cylindrical press. This was capable of printing 8,000 sheets per hour. This press was particularly useful for printing newspapers. In the late nineteenth century, the offset press was developed which could print up to six colours at a time. From the turn of the twentieth century, electrically operated presses accelerated printing operations. A series of other developments followed. Methods of feeding paper improved, the quality of plates became better, automatic paper reels and photoelectric controls of the colour register were introduced. The accumulation of several individual mechanical improvements transformed the appearance of printed texts. Printers and publishers continuously developed new strategies to sell their product. Nineteenth-century periodicals serialised important novels, which gave birth to a particular way of writing novels. In the 1920s in England, popular works were sold in cheap series, called the Shilling Series. The dust cover or the book jacket is also a twentieth-century innovation. With the onset of the Great Depression in the 1930s, publishers feared a decline in book purchases. To sustain buying, they brought out cheap paperback editions. Look at Fig. 13. What impact do such advertisements have on the public mind? Do you think everyone reacts to printed material in the same way? Activity Fig. 13 Advertisements at a railway station in England, a lithograph by Alfred Concanen, 1874. 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STRUCTURE OF THE ATOM 53 Q Many elements consist of a mixture of isotopes. Each isotope of an element is a pure substance. The chemical properties of isotopes are similar but their physical properties are different. Chlorine occurs in nature in two isotopic forms, with masses 35 u and 37 u in the ratio of 31. Obviously, the question arises what should we take as the mass of chlorine atom? Let us find out. The average atomic mass of chlorine atom, on the basis of above data, will be 35 75 100 37 25 100 105 4 37 4 142 4 35 5 . u The mass of an atom of any natural element is taken as the average mass of all the naturally occuring atoms of that element. If an element has no isotopes, then the mass of its atom would be the same as the sum of protons and neutrons in it. But if an element occurs in isotopic forms, then we have to know the percentage of each isotopic form and then the average mass is calculated. This does not mean that any one atom of chlorine has a fractional mass of 35.5 u. It means that if you take a certain amount of chlorine, it will contain both isotopes of chlorine and the average mass is 35.5 u. Applications Since the chemical properties of all the isotopes of an element are the same, normally we are not concerned about taking a mixture. But some isotopes have special properties which find them useful in various fields. Some of them are (i) An isotope of uranium is used as a fuel in nuclear reactors. (ii) An isotope of cobalt is used in the treatment of cancer. (iii) An isotope of iodine is used in the treatment of goitre. 4.6.1 ISOBARS Let us consider two elements calcium, atomic number 20, and argon, atomic number 18. The number of protons in these atoms is different, but the mass number of both these elements is 40. That is, the total number of nucleons is the same in the atoms of this pair of elements. Atoms of different elements with different atomic numbers, which have the same mass number, are known as isobars. uestions 1. For the symbol H,D and T tabulate three sub-atomic particles found in each of them. 2. Write the electronic configuration of any one pair of isotopes and isobars. What you have learnt Credit for the discovery of electron and proton goes to J.J. Thomson and E.Goldstein, respectively. J.J. 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185 Novels, Society and History Women novelists George Eliot (1819-1880) was the pen-name of Mary Ann Evans. A very popular novelist, she believed that novels gave women a special opportunity to express themselves freely. Every woman could see herself as capable of writing fiction Fiction is a department of literature in which women can, after their kind, fully equal men No educational restrictions can shut women from the materials of fiction, and there is no species of art that is so free from rigid requirements. George Eliot, Silly novels by lady novelists, 1856. Box 1 1.5 Novels for the Young Novels for young boys idealised a new type of man someone who was powerful, assertive, independent and daring. Most of these novels were full of adventure set in places remote from Europe. The colonisers appear heroic and honourable confronting native peoples and strange surroundings, adapting to native life as well as changing it, colonising territories and then developing nations there. Books like R.L. Stevensons Treasure Island (1883) or Rudyard Kiplings Jungle Book (1894) became great hits. G.A. Hentys historical adventure novels for boys were also wildly popular during the height of the British empire. They aroused the excitement and adventure of conquering strange lands. They were set in Mexico, Alexandria, Siberia and many other countries. They were always about young boys who witness grand historical events, get involved in some military action and show what they called English courage. Love stories written for adolescent girls also first became popular in this period, especially in the US, notably Ramona (1884) by Helen Hunt Jackson and a series entitled What Katy Did (1872) by Sarah Chauncey Woolsey, who wrote under the pen-name Susan Coolidge. G.A. Henty (1832-1902) In Under Drakes Flag (1883) two young Elizabethan adventurers face their apparently approaching death, but still remember to assert their Englishness Well, Ned, we have had more good fortune than we could have expected. We might have been killed on the day when we landed, and we have spent six jolly months in wandering together as hunters on the plain. If we must die, let us behave like Englishmen and Christians. Box 2 Fig. 13 Charlotte Bronte (1816-1855). Aunt who is always unkind to her People think you a good woman, but you are bad ... You are deceitful! 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SCIENCE 152 uestions 1. What is the kinetic energy of an object? 2. Write an expression for the kinetic energy of an object. 3. The kinetic energy of an object of mass, m moving with a velocity of 5 m s1 is 25 J. What will be its kinetic energy when its velocity is doubled? What will be its kinetic energy when its velocity is increased three times? 11.2.3 POTENTIAL ENERGY Activity 11.8 Take a rubber band. Hold it at one end and pull from the other. The band stretches. Release the band at one of the ends. What happens? The band will tend to regain its original length. Obviously the band had acquired energy in its stretched position. How did it acquire energy when stretched? Activity 11.9 Take a slinky as shown below. Ask a friend to hold one of its ends. You hold the other end and move away from your friend. Now you release the slinky. Activity 11.11 Lift an object through a certain height. The object can now do work. It begins to fall when released. This implies that it has acquired some energy. If raised to a greater height it can do more work and hence possesses more energy. From where did it get the energy? Think and discuss. In the above situations, the energy gets stored due to the work done on the object. The energy transferred to an object is stored as potential energy if it is not used to cause a change in the velocity or speed of the object. You transfer energy when you stretch a rubber band. The energy transferred to the band is its potential energy. You do work while winding the key of a toy car. The energy transferred to the spring inside is stored as potential energy. The potential energy possessed by the object is the energy present in it by virtue of its position or configuration. Activity 11.12 Take a bamboo stick and make a bow as shown in Fig. 11.6. Place an arrow made of a light stick on it with one end supported by the stretched string. Now stretch the string and release the arrow. Notice the arrow flying off the bow. Notice the change in the shape of the bow. The potential energy stored in the bow due to the change of shape is thus used in the form of kinetic energy in throwing off the arrow. Q Fig.11.6 An arrow and the stretched string on the bow. What happened? How did the slinky acquire energy when stretched? Would the slinky acquire energy when it is compressed? Activity 11.10 Take a toy car. Wind it using its key. Place the car on the ground. Did it move? From where did it acquire energy? Does the energy acquired depend on the number of windings? 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PROOFS IN MATHEMATICS 319 Number of points Number of regions 1 1 2 2 3 4 4 8 5 6 7 Some of you might have come up with a formula predicting the number of regions given the number of points. From Class IX, you may remember that this intelligent guess is called a conjecture. Suppose your conjecture is that given n points on a circle, there are 2n 1 mutually exclusive regions, created by joining the points with all possible lines. This seems an extremely sensible guess, and one can check that if n 5, we do get 16 regions. So, having verified this formula for 5 points, are you satisfied that for any n points there are 2n 1 regions? If so, how would you respond, if someone asked you, how you can be sure about this for n 25, say? To deal with such questions, you would need a proof which shows beyond doubt that this result is true, or a counter- example to show that this result fails for some n. Actually, if you are patient and try it out for n 6, you will find that there are 31 regions, and for n 7 there are 57 regions. So, n 6, is a counter-example to the conjecture above. This demonstrates the power of a counter-example. You may recall that in the Class IX we discussed that to disprove a statement, it is enough to come up with a single counter- example. You may have noticed that we insisted on a proof regarding the number of regions in spite of verifying the result for n 1, 2, 3, 4 and 5. Let us consider a few more examples. You are familiar with the following result (given in Chapter 5) 1 2 3 ... n ( 1) 2 n n . To establish its validity, it is not enough to verify the result for n 1, 2, 3, and so on, because there may be some n for which this result is not true (just as in the example above, the result failed for n 6). What we need is a proof which establishes its truth beyond doubt. 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Science 6. The position of three elements A, B and C in the Periodic Table are shown below Group 16 Group 17 - - - A - - B C (a) State whether A is a metal or non-metal. (b) State whether C is more reactive or less reactive than A. (c) Will C be larger or smaller in size than B? (d) Which type of ion, cation or anion, will be formed by element A? 7. Nitrogen (atomic number 7) and phosphorus (atomic number 15) belong to group 15 of the Periodic Table. Write the electronic configuration of these two elements. Which of these will be more electronegative? Why? 8. How does the electronic configuration of an atom relate to its position in the Modern Periodic Table? 9. In the Modern Periodic Table, calcium (atomic number 20) is surrounded by elements with atomic numbers 12, 19, 21 and 38. Which of these have physical and chemical properties resembling calcium? 10. Compare and contrast the arrangement of elements in Mendelevs Periodic Table and the Modern Periodic Table. I We have discussed the major attempts made for classifying elements. Find out (from the internet or library) about other attempts to classify elements. II We have studied the long form of the Periodic Table. The Modern Periodic Law has been used to arrange elements in other ways too. 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264 MATHEMATICS The third step is to find the product of di with the corresponding fi, and take the sum of all the fi dis. The calculations are shown in Table 14.4. Table 14.4 Class interval Number of Class mark di xi 47.5 fidi students ( fi) (xi) 10 - 25 2 17.5 30 60 25 - 40 3 32.5 15 45 40 - 55 7 47.5 0 0 55 - 70 6 62.5 15 90 70 - 85 6 77.5 30 180 85 - 100 6 92.5 45 270 Total fi 30 fidi 435 So, from Table 14.4, the mean of the deviations, d i i i f d f . Now, let us find the relation between d and x . Since in obtaining di, we subtracted a from each xi, so, in order to get the mean x , we need to add a to d . This can be explained mathematically as Mean of deviations, d i i i f d f So, d ( ) i i i f x a f i i i i i f x f a f f i i f x a f x a So, x a d i.e., x i i i f d a f 2019-20	[ 17, 21, 19, 24795, 1799, 56889, 19100, 576, 4843, 3019, 374, 311, 1477, 279, 1985, 315, 1853, 448, 279, 12159, 9136, 11, 323, 1896, 279, 2629, 315, 678, 279, 9136, 827, 13, 576, 28117, 525, 6839, 304, 6633, 220, 16, 19, 13, 19, 13, 6633, 220, 16, 19, 13, 19, 3228, 9873, 5624, 315, 3228, 1868, 1853, 37590, 220, 19, 22, 13, 20, 282, 12278, 4143, 320, 9136, 8, 320, 11665, 8, 220, 16, 15, 481, 220, 17, 20, 220, 17, 220, 16, 22, 13, 20, 220, 18, 15, 220, 21, 15, 220, 17, 20, 481, 220, 19, 15, 220, 18, 220, 18, 17, 13, 20, 220, 16, 20, 220, 19, 20, 220, 19, 15, 481, 220, 20, 20, 220, 22, 220, 19, 22, 13, 20, 220, 15, 220, 15, 220, 20, 20, 481, 220, 22, 15, 220, 21, 220, 21, 17, 13, 20, 220, 16, 20, 220, 24, 15, 220, 22, 15, 481, 220, 23, 20, 220, 21, 220, 22, 22, 13, 20, 220, 18, 15, 220, 16, 23, 15, 220, 23, 20, 481, 220, 16, 15, 15, 220, 21, 220, 24, 17, 13, 20, 220, 19, 20, 220, 17, 22, 15, 10657, 9136, 220, 18, 15, 282, 12278, 220, 19, 18, 20, 2055, 11, 504, 6633, 220, 16, 19, 13, 19, 11, 279, 3076, 315, 279, 85265, 11, 294, 600, 600, 600, 282, 294, 282, 659, 4695, 11, 1077, 601, 1477, 279, 12687, 1948, 294, 323, 856, 659, 8704, 304, 19009, 1853, 11, 582, 32256, 291, 264, 504, 1817, 37590, 11, 773, 11, 304, 1973, 311, 633, 279, 3076, 856, 1154, 582, 1184, 311, 912, 264, 311, 294, 659, 1096, 646, 387, 11247, 6888, 336, 7022, 438, 16327, 315, 85265, 11, 294, 600, 600, 600, 282, 294, 282, 2055, 11, 294, 320, 873, 600, 600, 600, 282, 856, 264, 282, 600, 600, 600, 600, 600, 282, 856, 282, 264, 282, 282, 600, 600, 282, 856, 264, 282, 856, 264, 2055, 11, 856, 264, 294, 600, 1734, 2572, 856, 600, 600, 600, 282, 294, 264, 282, 220, 17, 15, 16, 24, 12, 17, 15, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645 ]	[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
Socialism in Europe and the Russian Revolution 27 Almost all industries were the property of individuals. Liberals and radicals themselves were often property owners and employers. Having made their wealth through trade or industrial ventures, they felt that such effort should be encouraged that its benefits would be achieved if the workforce in the economy was healthy and citizens were educated. Opposed to the privileges the old aristocracy had by birth, they firmly believed in the value of individual effort, labour and enterprise. If freedom of individuals was ensured, if the poor could labour, and those with capital could operate without restraint, they believed that societies would develop. Many working men and women who wanted changes in the world rallied around liberal and radical groups and parties in the early nineteenth century. Some nationalists, liberals and radicals wanted revolutions to put an end to the kind of governments established in Europe in 1815. In France, Italy, Germany and Russia, they became revolutionaries and worked to overthrow existing monarchs. Nationalists talked of revolutions that would create nations where all citizens would have Fig.1 The London poor in the mid-nineteenth century as seen by a contemporary. 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India and the Contemporary World 74 4 Rebuilding a World Economy The Post-war Era The Second World War broke out a mere two decades after the end of the First World War. It was fought between the Axis powers (mainly Nazi Germany, Japan and Italy) and the Allies (Britain, France, the Soviet Union and the US). It was a war waged for six years on many fronts, in many places, over land, on sea, in the air. Once again death and destruction was enormous. At least 60 million people, or about 3 per cent of the worlds 1939 population, are believed to have been killed, directly or indirectly, as a result of the war. Millions more were injured. Unlike in earlier wars, most of these deaths took place outside the battlefields. Many more civilians than soldiers died from war-related causes. Vast parts of Europe and Asia were devastated, and several cities were destroyed by aerial bombardment or relentless artillery attacks. The war caused an immense amount of economic devastation and social disruption. Reconstruction promised to be long and difficult. Two crucial influences shaped post-war reconstruction. The first was the USs emergence as the dominant economic, political and military power in the Western world. The second was the dominance of the Soviet Union. It had made huge sacrifices to defeat Nazi Germany, and transformed itself from a backward agricultural country into a world power during the very years when the capitalist world was trapped in the Great Depression. 4.1 Post-war Settlement and the Bretton Woods Institutions Economists and politicians drew two key lessons from inter-war economic experiences. First, an industrial society based on mass production cannot be sustained without mass consumption. But to ensure mass consumption, there was a need for high and stable incomes. Incomes could not be stable if employment was unstable. Thus stable incomes also required steady, full employment. But markets alone could not guarantee full employment. Therefore governments would have to step in to minimise Fig. 24 German forces attack Russia, July 1941. Hitlers attempt to invade Russia was a turning point in the war. 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Science 4. Explain the nature of the covalent bond using the bond formation in CH3Cl. 5. Draw the electron dot structures for (a) ethanoic acid. (b) H2S. (c) propanone. (d) F2 . 6. What is an homologous series? Explain with an example. 7. How can ethanol and ethanoic acid be differentiated on the basis of their physical and chemical properties? 8. Why does micelle formation take place when soap is added to water? Will a micelle be formed in other solvents such as ethanol also? 9. Why are carbon and its compounds used as fuels for most applications? 10. Explain the formation of scum when hard water is treated with soap. 11. What change will you observe if you test soap with litmus paper (red and blue)? 12. What is hydrogenation? What is its industrial application? 13. Which of the following hydrocarbons undergo addition reactions C2H6, C3H8, C3H6, C2H2 and CH4. 14. Give a test that can be used to differentiate between saturated and unsaturated hydrocarbons. 15. Explain the mechanism of the cleaning action of soaps. I Use molecular model kits to make models of the compounds you have learnt in this Chapter. II Take about 20 mL of castor oilcotton seed oillinseed oilsoyabean oil in a beaker. Add 30 mL of 20 sodium hydroxide solution. Heat the mixture with continuous stirring for a few minutes till the mixture thickens. Add 5-10 g of common salt to this. Stir the mixture well and allow it to cool. You can cut out the soap in fancy shapes. 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24 MATHEMATICS Case (i) Here, the graph cuts x-axis at two distinct points A and A. The x-coordinates of A and A are the two zeroes of the quadratic polynomial ax2 bx c in this case (see Fig. 2.3). Fig. 2.3 Case (ii) Here, the graph cuts the x-axis at exactly one point, i.e., at two coincident points. So, the two points A and A of Case (i) coincide here to become one point A (see Fig. 2.4). 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320 MATHEMATICS Now, consider Fig. A1.3, where PQ and PR are tangents to the circle drawn from P. You have proved that PQ PR (Theorem 10.2). You were not satisfied by only drawing several such figures, measuring the lengths of the respective tangents, and verifying for yourselves that the result was true in each case. Do you remember what did the proof consist of ? It consisted of a sequence of statements (called valid arguments), each following from the earlier statements in the proof, or from previously proved (and known) results independent from the result to be proved, or from axioms, or from definitions, or from the assumptions you had made. And you concluded your proof with the statement PQ PR, i.e., the statement you wanted to prove. This is the way any proof is constructed. We shall now look at some examples and theorems and analyse their proofs to help us in getting a better understanding of how they are constructed. We begin by using the so-called direct or deductive method of proof. In this method, we make several statements. Each is based on previous statements. If each statement is logically correct (i.e., a valid argument), it leads to a logically correct conclusion. Example 10 The sum of two rational numbers is a rational number. Solution S.No. Statements AnalysisComments 1. Let x and y be rational numbers. Since the result is about rationals, we start with x and y which are rational. 2. Let m x n , n 0 and p y q , q 0 where m, n, p and q are integers. 3. So, m p mq np x y n q nq Fig. A1.3 Apply the definition of rationals. 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REAL NUMBERS 3 moment we write down such equations we are using Euclids division lemma, which is given in Theorem 1.1. Getting back to our puzzle, do you have any idea how you will solve it? Yes! You must look for the multiples of 7 which satisfy all the conditions. By trial and error (using the concept of LCM), you will find he had 119 eggs. In order to get a feel for what Euclids division lemma is, consider the following pairs of integers 17, 6 5, 12 20, 4 Like we did in the example, we can write the following relations for each such pair 17 6 2 5 (6 goes into 17 twice and leaves a remainder 5) 5 12 0 5 (This relation holds since 12 is larger than 5) 20 4 5 0 (Here 4 goes into 20 five-times and leaves no remainder) That is, for each pair of positive integers a and b, we have found whole numbers q and r, satisfying the relation a bq r, 0 r b Note that q or r can also be zero. Why dont you now try finding integers q and r for the following pairs of positive integers a and b? (i) 10, 3 (ii) 4, 19 (iii) 81, 3 Did you notice that q and r are unique? These are the only integers satisfying the conditions a bq r, where 0 r b. You may have also realised that this is nothing but a restatement of the long division process you have been doing all these years, and that the integers q and r are called the quotient and remainder, respectively. A formal statement of this result is as follows Theorem 1.1 (Euclids Division Lemma) Given positive integers a and b, there exist unique integers q and r satisfying a bq r, 0 r b. This result was perhaps known for a long time, but was first recorded in Book VII of Euclids Elements. 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INTRODUCTION TO TRIGONOMETRY 173 8 There is perhaps nothing which so occupies the middle position of mathematics as trigonometry. J.F. Herbart (1890) 8.1 Introduction You have already studied about triangles, and in particular, right triangles, in your earlier classes. Let us take some examples from our surroundings where right triangles can be imagined to be formed. For instance 1. Suppose the students of a school are visiting Qutub Minar. Now, if a student is looking at the top of the Minar, a right triangle can be imagined to be made, as shown in Fig 8.1. Can the student find out the height of the Minar, without actually measuring it? 2. Suppose a girl is sitting on the balcony of her house located on the bank of a river. She is looking down at a flower pot placed on a stair of a temple situated nearby on the other bank of the river. A right triangle is imagined to be made in this situation as shown in Fig.8.2. If you know the height at which the person is sitting, can you find the width of the river? 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India and the Contemporary World 40 with the British, as they had done in 1921-22, but also to break colonial laws. Thousands in different parts of the country broke the salt law, manufactured salt and demonstrated in front of government salt factories. As the movement spread, foreign cloth was boycotted, and liquor shops were picketed. Peasants refused to pay revenue and chaukidari taxes, village officials resigned, and in many places forest people violated forest laws going into Reserved Forests to collect wood and graze cattle. Worried by the developments, the colonial government began arresting the Congress leaders one by one. This led to violent clashes in many palaces. When Abdul Ghaffar Khan, a devout disciple of Mahatma Gandhi, was arrested in April 1930, angry crowds demonstrated in the streets of Peshawar, facing armoured cars and police firing. Many were killed. A month later, when Mahatma Gandhi himself was arrested, industrial workers in Sholapur attacked police posts, municipal buildings, lawcourts and railway stations all structures that symbolised British rule. A frightened government responded with a policy of brutal repression. Peaceful satyagrahis were attacked, women and children were beaten, and about 100,000 people were arrested. In such a situation, Mahatma Gandhi once again decided to call off the movement and entered into a pact with Irwin on 5 March 1931. By this Gandhi-Irwin Pact, Gandhiji consented to participate in a Round Table Conference (the Congress had boycotted the first Fig. 7 The Dandi march. During the salt march Mahatma Gandhi was accompanied by 78 volunteers. On the way they were joined by thousands. 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LINEAR EQUATIONS IN TWO VARIABLES 71 In the previous chapter, you studied how to plot the points on a graph paper. Let us plot the points (0, 3), (2, 2), (4, 1) and (6, 0) on a graph paper. Now join any two of these points and obtain a line. Let us call this as line AB (see Fig. 4.2). Do you see that the other two points also lie on the line AB? Now, pick another point on this line, say (8, 1). Is this a solution? In fact, 8 2(1) 6. So, (8, 1) is a solution. Pick any other point on this line AB and verify whether its coordinates satisfy the equation or not. Now, take any point not lying on the line AB, say (2, 0). Do its coordinates satisfy the equation? Check, and see that they do not. Let us list our observations 1. Every point whose coordinates satisfy Equation (1) lies on the line AB. 2. Every point (a, b) on the line AB gives a solution x a, y b of Equation (1). 3. Any point, which does not lie on the line AB, is not a solution of Equation (1). So, you can conclude that every point on the line satisfies the equation of the line and every solution of the equation is a point on the line. In fact, a linear equation in two variables is represented geometrically by a line whose points make up the collection of solutions of the equation. This is called the graph of the linear equation. So, to obtain the graph of a linear equation in two variables, it is enough to plot two points corresponding to two solutions and join them by a line. However, it is advisable to plot more than two such points so that you can immediately check the correctness of the graph. Remark The reason that a, degree one, polynomial equation ax by c 0 is called a linear equation is that its geometrical representation is a straight line. Example 5 Given the point (1, 2), find the equation of a line on which it lies. How many such equations are there? Solution Here (1, 2) is a solution of a linear equation you are looking for. So, you are looking for any line passing through the point (1, 2). One example of such a linear equation is x y 3. Others are y x 1, y 2x, since they are also satisfied by the coordinates of the point (1, 2). 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Science Figure 13.20 gives a schematic diagram of one of the common domestic circuits. In each separate circuit, different appliances can be connected across the live and neutral wires. Each appliance has a separate switch to ONOFF the flow of current through it. In order that each appliance has equal potential difference, they are connected parallel to each other. Electric fuse is an important component of all domestic circuits. We have already studied the principle and working of a fuse in the previous chapter (see Section 12.7). A fuse in a circuit prevents damage to the appliances and the circuit due to overloading. Overloading can occur when the live wire and the neutral wire come into direct contact. (This occurs when the insulation of wires is damaged or there is a fault in the appliance.) In such a situation, the current in the circuit abruptly increases. This is called short-circuiting. The use of an electric fuse prevents the electric circuit and the appliance from a possible damage by stopping the flow of unduly high electric current. The Joule heating that takes place in the fuse melts it to break the electric circuit. Overloading can also occur due to an accidental hike in the supply voltage. Sometimes overloading is caused by connecting too many appliances to a single socket. Figure 13.20 Figure 13.20 Figure 13.20 Figure 13.20 Figure 13.20 A schematic diagram of one of the common domestic circuits 1. Name two safety measures commonly used in electric circuits and appliances. 2. An electric oven of 2 kW power rating is operated in a domestic electric circuit (220 V) that has a current rating of 5 A. What result do you expect? Explain. 3. 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22 MATHEMATICS (iii) ( ) ( ) a b a b a b (iv) ( ) ( ) 2 a b a b a b (v) ( ) ( ) a b c d ac ad bc bd (vi) ( ) 2 2 a b a ab b Let us look at some particular cases of these identities. Example 16 Simplify the following expressions (i) ( ) ( ) 5 7 2 5 (ii) ( ) ( ) 5 5 5 5 (iii) ( ) 2 3 7 (iv) ( ) ( ) 11 7 11 7 Solution (i) ( ) ( ) 5 7 2 5 10 5 5 2 7 35 (ii) ( ) ( ) ( ) 2 2 5 5 5 5 5 5 25 5 20 (iii) ( ) ( ) ( ) 2 2 2 3 7 3 2 3 7 7 3 2 21 7 10 2 21 (iv) ( ) ( ) ( ) ( ) 2 2 11 7 11 7 11 7 11 7 4 Remark Note that simplify in the example above has been used to mean that the expression should be written as the sum of a rational and an irrational number. We end this section by considering the following problem. Look at 1 2 Can you tell where it shows up on the number line? You know that it is irrational. May be it is easier to handle if the denominator is a rational number. Let us see, if we can rationalise the denominator, that is, to make the denominator into a rational number. To do so, we need the identities involving square roots. Let us see how. Example 17 Rationalise the denominator of 1 2 Solution We want to write 1 2 as an equivalent expression in which the denominator is a rational number. We know that 2 . 2 is rational. 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Democracy and Diversity 31 The International Olympic Association held Carlos and Smith guilty of violating the Olympic spirit by making a political statement. Their medals were taken back. Back home, they were subjected to a lot of criticism. Norman too suffered for his action and was not included in the Australian team for the next Olympic. But their action succeeded in gaining international attention for the Civil Rights Movement in the US. Recently, the San Jose (pronounced Saan Hoze) State University, of which they were former students, honoured them and installed their statue in the University campus. When Norman died in 2006, Smith and Carlos were pallbearers at his funeral. Some Dalit groups decided to participate in the UN Conference Against Racism in Durban in 2001, demanding the inclusion of caste in the agenda of this conference. Here are three reactions to this move Amandeep Kaur (a government official) Our Constitution declares caste discrimination to be illegal. If some caste discrimination continues, it is an internal matter. I am opposed to this being raised in an international forum. Oinam (a sociologist) I am opposed to this because caste and race are not similar divisions. Caste is a social division, while race is a biological one. Raising caste in this conference on racism would mean equating the two. Ashok (a Dalit activist) The argument about internal matter is a way of preventing open discussion of oppression and discrimination. Race is not purely biological. It is as much a legal and sociological category as caste. Caste discrimination must be raised in this conference. Which of the three opinions do you agree with most and why? Differences, similarities, divisions The athletes in the example above were responding to social divisions and social inequalities. But does that happen only in societies which have racial divisions? In the previous two chapters we have already noted some other forms of social divisions. The examples of Belgium and Sri Lanka show both regional and social divisions. In the case of Belgium we noted that people who live in different regions speak different languages. In Sri Lanka, we noted linguistic as well as religious differences. Thus social diversity can take different forms in different societies. I met this group of girls from Pakistan and felt that I had more in common with them than many girls from other parts of my own country. 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153 Print Culture It is difficult for us to imagine a world without printed matter. We find evidence of print everywhere around us in books, journals, newspapers, prints of famous paintings, and also in everyday things like theatre programmes, official circulars, calendars, diaries, advertisements, cinema posters at street corners. We read printed literature, see printed images, follow the news through newspapers, and track public debates that appear in print. We take for granted this world of print and often forget that there was a time before print. We may not realise that print itself has a history which has, in fact, shaped our contemporary world. What is this history? When did printed literature begin to circulate? How has it helped create the modern world? In this chapter we will look at the development of print, from its beginnings in East Asia to its expansion in Europe and in India. We will understand the impact of the spread of technology and consider how social lives and cultures changed with the coming of print. Print Culture a n d the Modern World Chapter VII Print Culture and the Modern World Fig. 1 Book making before the age of print, from Akhlaq-i-Nasiri, 1595. This is a royal workshop in the sixteenth century, much before printing began in India. You can see the text being dictated, written and illustrated. The art of writing and illustrating by hand was important in the age before print. 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choose. There is no one to stop them from using unfair means to get their money back. Compared to the formal lenders, most of the informal lenders charge a much higher interest on loans. Thus, the cost to the borrower of informal loans is much higher. Higher cost of borrowing means a larger part of the earnings of the borrowers is used to repay the loan. Hence, borrowers have less income left for themselves (as we saw for Shyamal in Sonpur). In certain cases, the high interest rate for borrowing can mean that the amount to be repaid is greater than the income of the borrower. This could lead to increasing debt (as we saw for Rama in Sonpur) and debt trap. Also, people who might wish to start an enterprise by borrowing may not do so because of the high cost of borrowing. For these reasons, banks and cooperative societies need to lend more. This would lead to higher incomes and many people could then borrow cheaply for a variety of needs. They could grow crops, do business, set up small-scale industries etc. They could set up new industries or trade in goods. Cheap and affordable credit is crucial for the countrys develop- ment. Graph 2 shows the importance of formal and informal sources of credit for people in urban areas. The people are divided into four groups, from poor to rich, as shown in the figure. You can see that 85 per cent of the loans taken by poor households in the urban areas are from informal sources. Compare this with the rich urban households. What do you find? Only 10 per cent of their loans are from informal sources, while 90 per cent are from formal sources. A similar pattern is also found in rural areas. The rich households are availing cheap credit from formal lenders whereas the poor households have to pay a large amount for borrowing. What does all this suggest? First, the formal sector still meets only about half of the total credit needs of the rural people. The remaining credit needs are met from informal sources. Graph 2 Of all the loans taken by urban housholds, what percentage was formal and what percentage was informal? poor households well-off rich housholds with few assets households households BLUE Per cent of loans from the INFORMAL sector 85 15 PURPLE Per cent of loans from the FORMAL sector 10 90 72 28 53 47 2019-20	[ 27052, 13, 2619, 374, 902, 825, 311, 2936, 1105, 504, 1667, 27643, 3363, 311, 633, 862, 3220, 1182, 13, 58713, 311, 279, 15908, 45015, 11, 1429, 315, 279, 41787, 45015, 6757, 264, 1753, 5080, 2734, 389, 16606, 13, 14301, 11, 279, 2783, 311, 279, 69619, 315, 41787, 16606, 374, 1753, 5080, 13, 34221, 2783, 315, 52575, 3363, 264, 8131, 949, 315, 279, 23681, 315, 279, 63388, 374, 1483, 311, 53338, 279, 11679, 13, 31040, 11, 63388, 614, 2686, 7911, 2115, 369, 5577, 320, 300, 582, 5485, 369, 1417, 88, 309, 278, 304, 11840, 24998, 568, 758, 3654, 5048, 11, 279, 1550, 2734, 4379, 369, 52575, 646, 3076, 429, 279, 3311, 311, 387, 2064, 3779, 374, 7046, 1091, 279, 7911, 315, 279, 69619, 13, 1096, 1410, 2990, 311, 7703, 11636, 320, 300, 582, 5485, 369, 431, 3029, 304, 11840, 24998, 8, 323, 11636, 22862, 13, 7281, 11, 1251, 879, 2578, 6426, 311, 1191, 458, 20179, 553, 52575, 1231, 537, 653, 773, 1576, 315, 279, 1550, 2783, 315, 52575, 13, 1752, 1493, 7966, 11, 13959, 323, 47466, 33675, 1184, 311, 38480, 803, 13, 1096, 1035, 2990, 311, 5080, 45691, 323, 1657, 1251, 1410, 1221, 17193, 11872, 398, 369, 264, 8045, 315, 3880, 13, 2379, 1410, 3063, 30565, 11, 653, 2562, 11, 738, 705, 2613, 12934, 19102, 4992, 13, 2379, 1410, 738, 705, 501, 19102, 476, 6559, 304, 11561, 13, 35934, 323, 16637, 6668, 374, 16587, 369, 279, 2294, 39607, 2225, 12, 11288, 13, 12165, 220, 17, 4933, 279, 12650, 315, 15908, 323, 41787, 8173, 315, 6668, 369, 1251, 304, 15662, 5671, 13, 576, 1251, 525, 17779, 1119, 3040, 5203, 11, 504, 7852, 311, 9080, 11, 438, 6839, 304, 279, 7071, 13, 1446, 646, 1490, 429, 220, 23, 20, 817, 2889, 315, 279, 16606, 4429, 553, 7852, 28839, 304, 279, 15662, 5671, 525, 504, 41787, 8173, 13, 23768, 419, 448, 279, 9080, 15662, 28839, 13, 3555, 653, 498, 1477, 30, 8278, 220, 16, 15, 817, 2889, 315, 862, 16606, 525, 504, 41787, 8173, 11, 1393, 220, 24, 15, 817, 2889, 525, 504, 15908, 8173, 13, 362, 4428, 5383, 374, 1083, 1730, 304, 19082, 5671, 13, 576, 9080, 28839, 525, 1822, 14277, 11872, 6668, 504, 15908, 45015, 19853, 279, 7852, 28839, 614, 311, 2291, 264, 3460, 3311, 369, 52575, 13, 3555, 1558, 678, 419, 4190, 30, 5512, 11, 279, 15908, 10486, 2058, 20027, 1172, 911, 4279, 315, 279, 2790, 6668, 3880, 315, 279, 19082, 1251, 13, 576, 9664, 6668, 3880, 525, 2270, 504, 41787, 8173, 13, 12165, 220, 17, 4940, 678, 279, 16606, 4429, 553, 15662, 7696, 53119, 11, 1128, 11414, 572, 15908, 323, 1128, 11414, 572, 41787, 30, 7852, 28839, 1632, 12462, 9080, 7696, 53119, 448, 2421, 11770, 28839, 28839, 55892, 3616, 2889, 315, 16606, 504, 279, 1964, 10818, 969, 10486, 220, 23, 20, 220, 16, 20, 7330, 9515, 3616, 2889, 315, 16606, 504, 279, 434, 17012, 10486, 220, 16, 15, 220, 24, 15, 220, 22, 17, 220, 17, 23, 220, 20, 18, 220, 19, 22, 220, 17, 15, 16, 24, 12, 17, 15, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645 ]	[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
108 Democratic Politics Thinking about political reforms Each of these challenges is linked to the possibility of reforms. As mentioned above, we discuss challenges only because we think these can be overcome. Generally all the suggestions or proposals about overcoming various challenges to democracy are called democracy reform or political reform. We are not going to give here a list of desirable political reforms, for there cannot be any such list. If all the countries do not have the same challenges, it follows that everyone cannot follow the same recipe of political reforms. We cannot prescribe a procedure for car repair without knowing which model the car is, what the defect is and what tools are available, where the car has broken down, etc. Can we at least have a list of such reforms for our country in todays context? We can develop some proposals for reforms at the national level. But the real challenge of reforms may not lie at the national level. Some of the crucial questions need to be thought at the State or local level. Besides, such a list may become irrelevant after some time. So, instead of that let us think of some broad guidelines that can be kept in mind while devising ways and means for political reforms in India l It is very tempting to think of legal ways of reforming politics, to think of new laws to ban undesirable things. But this temptation needs to be resisted. No doubt, law has an important role to play in political reform. Carefully devised changes in law can help to discourage wrong political practices and encourage good ones. But legal-constitutional changes by themselves cannot overcome challenges to democracy. This is like the rules of cricket. A change in rules for LBW decisions helped to reduce negative batting tactics. But no one would ever think that the quality of cricket could be improved mainly through changes in the rules. This is to be done mainly by the players, coaches and administrators. Similarly, democratic reforms are to be carried out mainly by political activists, parties, movements and politically conscious citizens. l Any legal change must carefully look at what results it will have on politics. Sometimes the results may be counter-productive. For example, many states have banned people who have more than two children from contesting panchayat elections. This has resulted in denial of democratic opportunity to many poor and women, which was not intended. Generally, laws that seek to ban something are not very successful in politics. Laws that give political actors incentives to do good things have more chances of working. The best laws are those which empower people to carry out democratic reforms. The Right to Information Act is a good example of a law that empowers the people to find out what is happening in government and act as watchdogs of democracy. Such a law helps to control corruption and supplements the existing laws that banned corruption and imposed strict penalties. l Democratic reforms are to be brought about principally through political practice. Therefore, the main focus of political reforms should be on ways to strengthen democratic practice. As we discussed in the chapter on political parties, the most important concern should be to increase and improve the quality of political participation by ordinary citizens. l Any proposal for political reforms should think not only about what is a good solution but also about who will implement it and how. It is not very wise to think that the legislatures will pass legislations that go against the interest of all the political parties and MPs. But measures that rely on democratic movements, citizens organisations and the media are likely to succeed. Let us keep these general guidelines in mind and look at some specific instances of challenges to democracy that require some measure of reform. 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India and the Contemporary World 102 Write in brief Project 1. Give two examples of different types of global exchanges which took place before the seventeenth century, choosing one example from Asia and one from the Americas. 2. Explain how the global transfer of disease in the pre-modern world helped in the colonisation of the Americas. 3. Write a note to explain the effects of the following a) The British governments decision to abolish the Corn Laws. b) The coming of rinderpest to Africa. c) The death of men of working-age in Europe because of the World War. d) The Great Depression on the Indian economy. e) The decision of MNCs to relocate production to Asian countries. 4. Give two examples from history to show the impact of technology on food availability. 5. What is meant by the Bretton Woods Agreement? Find out more about gold and diamond mining in South Africa in the nineteenth century. Who controlled the gold and diamond companies? Who were the miners and what were their lives like? Write in brief Discuss 6. Imagine that you are an indentured Indian labourer in the Caribbean. Drawing from the details in this chapter, write a letter to your family describing your life and feelings. 7. Explain the three types of movements or flows within international economic exchange. Find one example of each type of flow which involved India and Indians, and write a short account of it. 8. Explain the causes of the Great Depression. 9. Explain what is referred to as the G-77 countries. In what ways can G-77 be seen as a reaction to the activities of the Bretton Woods twins? 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uestions 1. What are canal rays? 2. If an atom contains one electron and one proton, will it carry any charge or not? 4.2 The Structure of an Atom We have learnt Daltons atomic theory in Chapter 3, which suggested that the atom was indivisible and indestructible. But the discovery of two fundamental particles (electrons and protons) inside the atom, led to the failure of this aspect of Daltons atomic theory. It was then considered necessary to know how electrons and protons are arranged within an atom. For explaining this, many scientists proposed various atomic models. J.J. Thomson was the first one to propose a model for the structure of an atom. 4.2.1 THOMSONS MODEL OF AN ATOM Thomson proposed the model of an atom to be similar to that of a Christmas pudding. The electrons, in a sphere of positive charge, were like currants (dry fruits) in a spherical Christmas pudding. We can also think of a watermelon, the positive charge in the atom is spread all over like the red edible part of the watermelon, while the electrons are studded in the positively charged sphere, like the seeds in the watermelon (Fig. 4.1). Thomson proposed that (i) An atom consists of a positively charged sphere and the electrons are embedded in it. (ii) The negative and positive charges are equal in magnitude. So, the atom as a whole is electrically neutral. Although Thomsons model explained that atoms are electrically neutral, the results of experiments carried out by other scientists could not be explained by this model, as we will see below. 4.2.2 RUTHERFORDS MODEL OF AN ATOM Ernest Rutherford was interested in knowing how the electrons are arranged within an atom. Rutherford designed an experiment for this. In this experiment, fast moving alpha ()-particles were made to fall on a thin gold foil. He selected a gold foil because he wanted as thin a layer as possible. This gold foil was about 1000 atoms thick. -particles are doubly-charged helium ions. Since they have a mass of 4 u, the fast-moving -particles have a considerable amount of energy. It was expected that -particles would be deflected by the sub-atomic particles in the gold atoms. Since the -particles were much heavier than the protons, he did not expect to see large deflections. Q Fig.4.1 Thomsons model of an atom J.J. Thomson (1856- 1940), a British physicist, was born in Cheetham Hill, a suburb of Manchester, on 18 December 1856. He was awarded the Nobel prize in Physics in 1906 for his work on the discovery of electrons. He directed the Cavendish Laboratory at Cambridge for 35 years and seven of his research assistants subsequently won Nobel prizes. 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TRIANGLES 147 But AC2 AB2 BC2 (Given) (2) So, AC PR From (1) and (2) (3) Now, in ABC and PQR, AB PQ (By construction) BC QR (By construction) AC PR Proved in (3) above So, ABC PQR (SSS congruence) Therefore, B Q (CPCT) But Q 90 (By construction) So, B 90 Note Also see Appendix 1 for another proof of this theorem. Let us now take some examples to illustrate the use of these theorems. Example 10 In Fig. 6.48, ACB 90 and CD AB. Prove that 2 2 BC BD AD AC Solution ACD ABC (Theorem 6.7) So, AC AB AD AC or, AC2 AB . AD (1) Similarly, BCD BAC (Theorem 6.7) So, BC BA BD BC or, BC2 BA . BD (2) Therefore, from (1) and (2), 2 2 BC AC BA BD BD AB AD AD Example 11 A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches a window 6 m above the ground. Find the length of the ladder. 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90 MATHEMATICS formed between the horizontal and the line of sight. Plenty of other examples can be given where lines and angles are used. In the subsequent chapters of geometry, you will be using these properties of lines and angles to deduce more and more useful properties. Let us first revise the terms and definitions related to lines and angles learnt in earlier classes. 6.2 Basic Terms and Definitions Recall that a part (or portion) of a line with two end points is called a line-segment and a part of a line with one end point is called a ray. Note that the line segment AB is denoted by AB , and its length is denoted by AB. The ray AB is denoted by AB , and a line is denoted by AB . However, we will not use these symbols, and will denote the line segment AB, ray AB, length AB and line AB by the same symbol, AB. The meaning will be clear from the context. Sometimes small letters l, m, n, etc. will be used to denote lines. If three or more points lie on the same line, they are called collinear points otherwise they are called non-collinear points. Recall that an angle is formed when two rays originate from the same end point. The rays making an angle are called the arms of the angle and the end point is called the vertex of the angle. You have studied different types of angles, such as acute angle, right angle, obtuse angle, straight angle and reflex angle in earlier classes (see Fig. 6.1). (i) acute angle 0 x 90 (ii) right angle y 90 (iii) obtuse angle 90 z 180 (iv) straight angle s 180 (v) reflex angle 180 t 360 Fig. 6.1 Types of Angles 2019-2020	[ 24, 15, 24795, 1799, 56889, 19100, 14122, 1948, 279, 16202, 323, 279, 1555, 315, 13929, 13, 68389, 315, 1008, 10295, 646, 387, 2661, 1380, 5128, 323, 25941, 525, 1483, 13, 758, 279, 17420, 29632, 315, 17047, 11, 498, 686, 387, 1667, 1493, 5888, 315, 5128, 323, 25941, 311, 7681, 10521, 803, 323, 803, 5390, 5888, 13, 6771, 601, 1156, 64736, 279, 3793, 323, 17473, 5435, 311, 5128, 323, 25941, 49250, 304, 6788, 6846, 13, 220, 21, 13, 17, 14625, 19591, 323, 46513, 79540, 429, 264, 949, 320, 269, 13348, 8, 315, 264, 1555, 448, 1378, 835, 3501, 374, 2598, 264, 1555, 7806, 9070, 323, 264, 949, 315, 264, 1555, 448, 825, 835, 1459, 374, 2598, 264, 18299, 13, 7036, 429, 279, 1555, 10238, 14137, 374, 3371, 9253, 553, 14137, 1154, 323, 1181, 3084, 374, 3371, 9253, 553, 14137, 13, 576, 18299, 14137, 374, 3371, 9253, 553, 14137, 1154, 323, 264, 1555, 374, 3371, 9253, 553, 14137, 659, 4354, 11, 582, 686, 537, 990, 1493, 17738, 11, 323, 686, 78064, 279, 1555, 10238, 14137, 11, 18299, 14137, 11, 3084, 14137, 323, 1555, 14137, 553, 279, 1852, 7735, 11, 14137, 13, 576, 7290, 686, 387, 2797, 504, 279, 2266, 13, 17688, 2613, 11931, 326, 11, 296, 11, 308, 11, 4992, 13, 686, 387, 1483, 311, 78064, 5128, 13, 1416, 2326, 476, 803, 3501, 10246, 389, 279, 1852, 1555, 11, 807, 525, 2598, 4530, 88921, 3501, 5937, 807, 525, 2598, 2477, 1786, 965, 88921, 3501, 13, 79540, 429, 458, 9210, 374, 14122, 979, 1378, 44120, 81216, 504, 279, 1852, 835, 1459, 13, 576, 44120, 3259, 458, 9210, 525, 2598, 279, 11715, 315, 279, 9210, 323, 279, 835, 1459, 374, 2598, 279, 11936, 315, 279, 9210, 13, 1446, 614, 19476, 2155, 4494, 315, 25941, 11, 1741, 438, 29783, 9210, 11, 1290, 9210, 11, 4514, 810, 9210, 11, 7678, 9210, 323, 32666, 9210, 304, 6788, 6846, 320, 4060, 23095, 13, 220, 21, 13, 16, 568, 320, 72, 8, 29783, 9210, 220, 15, 856, 220, 24, 15, 320, 3808, 8, 1290, 9210, 379, 220, 24, 15, 320, 34594, 8, 4514, 810, 9210, 220, 24, 15, 1147, 220, 16, 23, 15, 320, 344, 8, 7678, 9210, 274, 220, 16, 23, 15, 320, 85, 8, 32666, 9210, 220, 16, 23, 15, 259, 220, 18, 21, 15, 23095, 13, 220, 21, 13, 16, 20768, 315, 7416, 642, 220, 17, 15, 16, 24, 12, 17, 15, 17, 15, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645 ]	[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
India and the Contemporary World 42 5.1 Other Ways of Becoming Modern Japan and China Early Vietnamese nationalists had a close relationship with Japan and China. They provided models for those looking to change, a refuge for those who were escaping French police, and a location where a wider Asian network of revolutionaries could be established. In the first decade of the twentieth century a go east movement became popular. In 1907-08 some 300 Vietnamese students went to Japan to acquire modern education. For many of them the primary objective was to drive out the French from Vietnam, overthrow the puppet emperor and re-establish the Nguyen dynasty that had been deposed by the French. These nationalists looked for foreign arms and help. They appealed to the Japanese as fellow Asians. Japan had modernised itself and had resisted colonisation by the West. Besides, its victory over Russia in 1907 proved its military capabilities. Vietnamese students established a branch of the Restoration Society in Tokyo but after 1908, the Japanese Ministry of Interior clamped down on them. Many, including Phan Boi Chau, were deported and forced to seek exile in China and Thailand. Developments in China also inspired Vietnamese nationalists. In 1911, the long established monarchy in China was overthrown by a popular movement under Sun Yat-sen, and a Republic was set up. Inspired by these developments, Vietnamese students organised the Association for the Restoration of Vietnam (Viet-Nam Quan Phuc Hoi). Now the nature of the anti-French independence movement changed. The objective was no longer to set up a constitutional monarchy but a democratic republic. Soon, however, the anti-imperialist movement in Vietnam came under a new type of leadership. Fig. 9 Cartoon of Vietnamese nationalists chasing away imperialists. 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SCIENCE 18 Q They cannot be separated from the mixture by the process of filtration. But, a special technique of separation known as centrifugation (perform activity 2.5), can be used to separate the colloidal particles. The components of a colloidal solution are the dispersed phase and the dispersion medium. The solute-like component or the dispersed particles in a colloid form the dispersed phase, and the component in which the dispersed phase is suspended is known as the dispersing medium. Colloids are classified according to the state (solid, liquid or gas) of the dispersing medium and the dispersed phase. A few common examples are given in Table 2.1. From this table you can see that they are very common everyday life. uestions 1. Differentiate between homogen- eous and heterogeneous mixtures with examples. 2. How are sol, solution and suspension different from each other? 3. To make a saturated solution, 36 g of sodium chloride is dissolved in 100 g of water at 293 K. Find its concentration at this temperature. Tyndall effect can be observed when sunlight passes through the canopy of a dense forest. In the forest, mist contains tiny droplets of water, which act as particles of colloid dispersed in air. Fig. 2.4 The Tyndall effect Properties of a colloid A colloid is a heterogeneous mixture. The size of particles of a colloid is too small to be individually seen by naked eyes. Colloids are big enough to scatter a beam of light passing through it and make its path visible. They do not settle down when left undisturbed, that is, a colloid is quite stable. Table 2.1 Common examples of colloids Dispersed Dispersing Type Example phase Medium Liquid Gas Aerosol Fog, clouds, mist Solid Gas Aerosol Smoke, automobile exhaust Gas Liquid Foam Shaving cream Liquid Liquid Emulsion Milk, face cream Solid Liquid Sol Milk of magnesia, mud Gas Solid Foam Foam, rubber, sponge, pumice Liquid Solid Gel Jelly, cheese, butter Solid Solid Solid Sol Coloured gemstone, milky glass 2019-2020	[ 3540, 56682, 220, 16, 23, 1207, 2379, 4157, 387, 18663, 504, 279, 20980, 553, 279, 1882, 315, 74938, 13, 1988, 11, 264, 3281, 14762, 315, 24737, 3881, 438, 73082, 768, 367, 320, 28488, 5702, 220, 17, 13, 20, 701, 646, 387, 1483, 311, 8651, 279, 80948, 25880, 18730, 13, 576, 6813, 315, 264, 80948, 25880, 6291, 525, 279, 76710, 10262, 323, 279, 85612, 11051, 13, 576, 2048, 1070, 12681, 3692, 476, 279, 76710, 18730, 304, 264, 1375, 51096, 1352, 279, 76710, 10262, 11, 323, 279, 3692, 304, 892, 279, 76710, 10262, 374, 21612, 374, 3881, 438, 279, 78735, 287, 11051, 13, 4254, 385, 3365, 525, 21091, 4092, 311, 279, 1584, 320, 31027, 11, 14473, 476, 6819, 8, 315, 279, 78735, 287, 11051, 323, 279, 76710, 10262, 13, 362, 2421, 4185, 10295, 525, 2661, 304, 6633, 220, 17, 13, 16, 13, 5542, 419, 1965, 498, 646, 1490, 429, 807, 525, 1602, 4185, 17778, 2272, 13, 220, 3045, 908, 220, 16, 13, 33396, 6493, 1948, 4998, 11706, 12, 384, 782, 323, 97782, 6514, 18513, 448, 10295, 13, 220, 17, 13, 2585, 525, 2048, 11, 6291, 323, 24301, 2155, 504, 1817, 1008, 30, 220, 18, 13, 2014, 1281, 264, 49485, 6291, 11, 220, 18, 21, 342, 315, 38595, 81782, 374, 55667, 304, 220, 16, 15, 15, 342, 315, 3015, 518, 220, 17, 24, 18, 730, 13, 7379, 1181, 19950, 518, 419, 9315, 13, 13897, 303, 541, 2456, 646, 387, 13166, 979, 39020, 16211, 1526, 279, 62971, 315, 264, 27950, 13638, 13, 758, 279, 13638, 11, 8600, 5610, 13673, 6973, 89492, 315, 3015, 11, 892, 1160, 438, 18730, 315, 1375, 51096, 76710, 304, 3720, 13, 23095, 13, 220, 17, 13, 19, 576, 13897, 303, 541, 2456, 11831, 315, 264, 1375, 51096, 362, 1375, 51096, 374, 264, 97782, 20980, 13, 576, 1379, 315, 18730, 315, 264, 1375, 51096, 374, 2238, 2613, 311, 387, 31299, 3884, 553, 19020, 6414, 13, 4254, 385, 3365, 525, 2409, 3322, 311, 44477, 264, 23418, 315, 3100, 12299, 1526, 432, 323, 1281, 1181, 1815, 9434, 13, 2379, 653, 537, 24729, 1495, 979, 2115, 2030, 380, 74225, 11, 429, 374, 11, 264, 1375, 51096, 374, 5008, 15175, 13, 6633, 220, 17, 13, 16, 7718, 10295, 315, 80948, 3365, 4093, 31290, 291, 4093, 31290, 287, 3990, 13383, 10262, 24355, 41258, 20854, 63150, 337, 58148, 11, 29514, 11, 8600, 22138, 20854, 63150, 337, 53204, 11, 34428, 17502, 20854, 41258, 76456, 1417, 2317, 12644, 41258, 41258, 5748, 32903, 43825, 11, 3579, 12644, 22138, 41258, 11473, 43825, 315, 8455, 288, 685, 11, 26183, 20854, 22138, 76456, 76456, 11, 22674, 11, 68348, 11, 281, 372, 558, 41258, 22138, 44382, 73139, 11, 17163, 11, 14100, 22138, 22138, 22138, 11473, 4254, 20394, 18747, 10812, 11, 7473, 7891, 8991, 220, 17, 15, 16, 24, 12, 17, 15, 17, 15, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645 ]	[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
xi Contents Foreword iii A Letter for You v How to Use this Book vii Unit I Chapter 1 Power-sharing 1 Chapter 2 Federalism 13 Unit II Chapter 3 Democracy and Diversity 29 Chapter 4 Gender, Religion and Caste 39 Unit III Chapter 5 Popular Struggles and Movements 57 Chapter 6 Political Parties 71 Unit IV Chapter 7 Outcomes of Democracy 89 Chapter 8 Challenges to Democracy 101 2018-19	[ 11665, 35862, 8207, 1158, 62093, 362, 26659, 369, 1446, 348, 2585, 311, 5443, 419, 5893, 3275, 72, 7954, 358, 15585, 220, 16, 7420, 54756, 220, 16, 15585, 220, 17, 12137, 2142, 220, 16, 18, 7954, 7946, 15585, 220, 18, 47089, 323, 64971, 220, 17, 24, 15585, 220, 19, 28217, 11, 43093, 323, 356, 5525, 220, 18, 24, 7954, 14429, 15585, 220, 20, 31395, 4509, 2596, 642, 323, 53285, 3723, 220, 20, 22, 15585, 220, 21, 30497, 59905, 220, 22, 16, 7954, 16824, 15585, 220, 22, 4371, 6579, 315, 47089, 220, 23, 24, 15585, 220, 23, 68678, 311, 47089, 220, 16, 15, 16, 220, 17, 15, 16, 23, 12, 16, 24, 151645, 151645, 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India and the Contemporary World 24 Box 3 Meanings of the symbols Attribute Significance Broken chains Being freed Breastplate with eagle Symbol of the German empire strength Crown of oak leaves Heroism Sword Readiness to fight Olive branch around the sword Willingness to make peace Black, red and gold tricolour Flag of the liberal-nationalists in 1848, banned by the Dukes of the German states Rays of the rising sun Beginning of a new era With the help of the chart in Box 3, identify the attributes of Veits Germania and interpret the symbolic meaning of the painting. In an earlier allegorical rendering of 1836, Veit had portrayed the Kaisers crown at the place where he has now located the broken chain. Explain the significance of this change. Activity Fig. 18 The fallen Germania, Julius Hbner, 1850. Describe what you see in Fig. 17. What historical events could Hbner be referring to in this allegorical vision of the nation? 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20 Economics consumption and processing of primary product and own account production of fixed assets. Education helps individual to make better use of the economic opportunities available before him. Education and skill are the major determinants of the earning of any individual in the market. A majority of women have meagre education and low skill formation. Women are paid low compared to men. Most women work where job security is not there. Various activities relating to legal protection is meagre. Employment in this sector is characterised by irregular and low income. In this sector there is an absence of basic facilities like maternity leave, childcare and other social security systems. However, women with high education and skill formation are paid at par with the men. Among the organised sector, teaching and medicine attract them the most. Some women have entered administrative and other services including job, that need high levels of scientific and technological competence. Ask your sister or your classmate what she would like to take up as a career? Quality of Population The quality of population depends upon the literacy rate, health of a person indicated by life expectancy and skill formation acquired by the people of the country. The quality of the poulation ultimately decides the growth rate of the country. Literate and healthy population are an asset. Education Sakals education in the initial years of his life bore him the fruits in the later years in terms of a good job and salary. We saw education was an important input for the growth of Sakal. It opened new horizon for him, provided new aspiration and developed values of life. Not only for Sakal, education contributes towards the growth of society also. It enhances the Due to historical and cultural reasons there is a division of labour between men and women in the family. Women generally look after domestic chores and men work in the fields. Sakals mother Sheela cooks food, cleans utensils, washes clothes, cleans the house and looks after her children. Sakals father Buta cultivates the field, sells the produce in the market and earns money for the family. Sheela is not paid for the services delivered for upbringing of the family. Buta earns money, which he spends on rearing his family. Women are not paid for their service delivered in the family. The household work done by women is not recognised in the National Income. Geeta, mother of Vilas, earned an income by selling fish. Thus women are paid for their work when they enter the labour market. Their earning like that of their male counterpart is determined on the basis of education and skill. Activity Visit a village or colony located near to your residential area and note down the various activities undertaken by the people of that village or colony. If this is not possible, ask your neighbour what is their profession? In which of the three sectors will you categorise their work? Say whether these activities are economic or non-economic activities Vilas sells fish in the village market. Vilas cooks food for his family. Sakal works in the private firm. 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Science Test the pH values of solutions given in Table 2.2. Record your observations. What is the nature of each substance on the basis of your observations? Figure 2.7 Figure 2.7 Figure 2.7 Figure 2.7 Figure 2.7 pH of some common substances shown on a pH paper (colours are only a rough guide) The strength of acids and bases depends on the number of H ions and OH ions produced, respectively. If we take hydrochloric acid and acetic acid of the same concentration, say one molar, then these produce different amounts of hydrogen ions. Acids that give rise to more H ions are said to be strong acids, and acids that give less H ions are said to be weak acids. Can you now say what weak and strong bases are? Are plants and animals pH sensitive? Our body works within the pH range of 7.0 to 7.8. Living organisms can survive only in a narrow range of pH change. When pH of rain water is less than 5.6, it is called acid rain. When acid rain flows into the rivers, it lowers the pH of the river water. The survival of aquatic life in such rivers becomes difficult. Table 2.2 S. 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CIRCLES 207 You might have seen a pulley fitted over a well which is used in taking out water from the well. Look at Fig. 10.2. Here the rope on both sides of the pulley, if considered as a ray, is like a tangent to the circle representing the pulley. Is there any position of the line with respect to the circle other than the types given above? You can see that there cannot be any other type of position of the line with respect to the circle. In this chapter, we will study about the existence of the tangents to a circle and also study some of their properties. 10.2 Tangent to a Circle In the previous section, you have seen that a tangent to a circle is a line that intersects the circle at only one point. To understand the existence of the tangent to a circle at a point, let us perform the following activities Activity 1 Take a circular wire and attach a straight wire AB at a point P of the circular wire so that it can rotate about the point P in a plane. Put the system on a table and gently rotate the wire AB about the point P to get different positions of the straight wire see Fig. 10.3(i). In various positions, the wire intersects the circular wire at P and at another point Q1 or Q2 or Q3, etc. In one position, you will see that it will intersect the circle at the point P only (see position AB of AB). This shows that a tangent exists at the point P of the circle. On rotating further, you can observe that in all other positions of AB, it will intersect the circle at P and at another point, say R1 or R2 or R3, etc. So, you can observe that there is only one tangent at a point of the circle. While doing activity above, you must have observed that as the position AB moves towards the position A B, the common point, say Q1, of the line AB and the circle gradually comes nearer and nearer to the common point P. Ultimately, it coincides with the point P in the position AB of AB. Again note, what happens if AB is rotated rightwards about P? The common point R3 gradually comes nearer and nearer to P and ultimately coincides with P. So, what we see is The tangent to a circle is a special case of the secant, when the two end points of its corresponding chord coincide. Fig. 10.3 (i) Fig. 10.2 The word tangent comes from the Latin word tangere, which means to touch and was introduced by the Danish mathematician Thomas Fineke in 1583. 2019-20	[ 34, 51840, 14017, 220, 17, 15, 22, 1446, 2578, 614, 3884, 264, 7737, 3179, 28341, 916, 264, 1632, 892, 374, 1483, 304, 4633, 700, 3015, 504, 279, 1632, 13, 9192, 518, 23095, 13, 220, 16, 15, 13, 17, 13, 5692, 279, 33420, 389, 2176, 11067, 315, 279, 7737, 3179, 11, 421, 6509, 438, 264, 18299, 11, 374, 1075, 264, 68660, 311, 279, 12671, 14064, 279, 7737, 3179, 13, 2160, 1052, 894, 2309, 315, 279, 1555, 448, 5091, 311, 279, 12671, 1008, 1091, 279, 4494, 2661, 3403, 30, 1446, 646, 1490, 429, 1052, 4157, 387, 894, 1008, 943, 315, 2309, 315, 279, 1555, 448, 5091, 311, 279, 12671, 13, 758, 419, 12453, 11, 582, 686, 3920, 911, 279, 13885, 315, 279, 21878, 805, 311, 264, 12671, 323, 1083, 3920, 1045, 315, 862, 5888, 13, 220, 16, 15, 13, 17, 40362, 306, 311, 264, 21224, 758, 279, 3681, 3772, 11, 498, 614, 3884, 429, 264, 68660, 311, 264, 12671, 374, 264, 1555, 429, 88184, 279, 12671, 518, 1172, 825, 1459, 13, 2014, 3535, 279, 13885, 315, 279, 68660, 311, 264, 12671, 518, 264, 1459, 11, 1077, 601, 2736, 279, 2701, 7488, 14981, 220, 16, 11778, 264, 26931, 9067, 323, 15498, 264, 7678, 9067, 14137, 518, 264, 1459, 393, 315, 279, 26931, 9067, 773, 429, 432, 646, 16919, 911, 279, 1459, 393, 304, 264, 11031, 13, 10224, 279, 1849, 389, 264, 1965, 323, 29273, 16919, 279, 9067, 14137, 911, 279, 1459, 393, 311, 633, 2155, 9892, 315, 279, 7678, 9067, 1490, 23095, 13, 220, 16, 15, 13, 18, 1956, 568, 758, 5257, 9892, 11, 279, 9067, 88184, 279, 26931, 9067, 518, 393, 323, 518, 2441, 1459, 1207, 16, 476, 1207, 17, 476, 1207, 18, 11, 4992, 13, 758, 825, 2309, 11, 498, 686, 1490, 429, 432, 686, 31796, 279, 12671, 518, 279, 1459, 393, 1172, 320, 4060, 2309, 14137, 315, 14137, 568, 1096, 4933, 429, 264, 68660, 6724, 518, 279, 1459, 393, 315, 279, 12671, 13, 1913, 41396, 4623, 11, 498, 646, 22986, 429, 304, 678, 1008, 9892, 315, 14137, 11, 432, 686, 31796, 279, 12671, 518, 393, 323, 518, 2441, 1459, 11, 1977, 431, 16, 476, 431, 17, 476, 431, 18, 11, 4992, 13, 2055, 11, 498, 646, 22986, 429, 1052, 374, 1172, 825, 68660, 518, 264, 1459, 315, 279, 12671, 13, 5976, 3730, 5702, 3403, 11, 498, 1969, 614, 13166, 429, 438, 279, 2309, 14137, 10797, 6974, 279, 2309, 362, 425, 11, 279, 4185, 1459, 11, 1977, 1207, 16, 11, 315, 279, 1555, 14137, 323, 279, 12671, 26024, 4041, 86820, 323, 86820, 311, 279, 4185, 1459, 393, 13, 54006, 11, 432, 22970, 3341, 448, 279, 1459, 393, 304, 279, 2309, 14137, 315, 14137, 13, 13759, 5185, 11, 1128, 8573, 421, 14137, 374, 45620, 1290, 4014, 911, 393, 30, 576, 4185, 1459, 431, 18, 26024, 4041, 86820, 323, 86820, 311, 393, 323, 13653, 22970, 3341, 448, 393, 13, 2055, 11, 1128, 582, 1490, 374, 576, 68660, 311, 264, 12671, 374, 264, 3281, 1142, 315, 279, 5701, 517, 11, 979, 279, 1378, 835, 3501, 315, 1181, 12159, 43221, 71259, 13, 23095, 13, 220, 16, 15 ]	[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
Food Security in India 45 Lets Discuss Does Ahmad have a regular income from rickshaw-pulling? How does the yellow card help Ahmad Story of Ahmad Ahmad is a rickshaw puller in Bangalore. He has shifted from Jhumri Taliah along with his 3 brothers, 2 sisters and old parents. He stays in a jhuggi. The survival of all members of his family depends on his daily earnings from pulling rickshaw. However, he does not have a secured employment and his earnings fluctuate every day. During some days he gets enough earning for him to save some amount after buying all his day-to-day necessities. On other days, he barely earns enough to buy his daily necessities. However, fortunately, Ahmad has a yellow card, which is PDS Card for below poverty line people. With this card, Ahmad gets sufficient quantity of wheat, rice, sugar and kerosene oil for his daily use. He gets these essentials at half of the market price. He purchases his monthly stock during a particular day when the ration shop is opened for below poverty people. In this way, Ahmad is able to eke out his survival with less than sufficient earnings for his big family where he is the only earning member. Lets Discuss Why is agriculture a seasonal activity? Why is Ramu unemployed for about four months in a year? What does Ramu do when he is unemployed? Who are supplementing income in Ramus family? Why does Ramu face difficulty when he is unable to have work? When is Ramu food insecure? run his family even with small earnings from rickshaw-pulling? The social composition along with the inability to buy food also plays a role in food insecurity. The SCs, STs and some sections of the OBCs (lower castes among them) who have either poor land-base or very low land productivity are prone to food insecurity. The people affected by natural disasters, who have to migrate to other areas in search of work, are also among the most food insecure people. A high incidence of malnutrition prevails among women. This is a matter of serious concern as it puts even the unborn baby at the risk of malnutrition. A large proportion of pregnant and nursing mothers and children under the age of 5 years constitute an important segment of the food insecure population. According to the National Health and Family Survey (NHFS) 199899, the number of such women and children is approximately 11 crore. The food insecure people are disproportionately large in some regions of the country, such as economically backward states with high incidence of poverty, tribal and remote areas, regions more prone to natural disasters etc. In fact, the states of Uttar Pradesh (eastern and south-eastern parts), Bihar, Jharkhand, Orissa, West Bengal, Chattisgarh, parts of Madhya Pradesh and Maharasthra account for largest number of food insecure people in the country. Hunger is another aspect indicating food insecurity. Hunger is not just an expression of poverty, it brings about poverty. The attainment of food security therefore involves eliminating current hunger and reducing the risks of future hunger. Hunger has chronic and seasonal dimensions. 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though industrial output or the production of goods went up by more than nine times during the period, employment in the industry went up by around three times. The same applies to the tertiary sector as well. While production in the service sector rose by 14 times, employment in the service sector rose around five times. As a result, more than half of the workers in the country are working in the primary sector, mainly in agriculture, producing only a quarter of the GDP. In contrast to this, the secondary and tertiary sectors produce four-fifths of the produce whereas they employ less than half the people. Does this mean that the workers in agriculture are not producing as much as they could? What it means is that there are more people in agriculture than is necessary. So, even if you move a few people out, production will not be affected. In other words, workers in the agricultural sector are underemployed. For instance, take the case of a small farmer, Laxmi, owning about two hectares of unirrigated land dependent only on rain and growing crops, like jowar and arhar. All five members of her family work in the plot throughout the year. Why? They have nowhere else to go for work. You will see that everyone is working, none remains idle, but in actual fact, their labour effort gets divided. Each one is doing some work but no one is fully employed. This is the situation of underemployment, where people are apparently working but all of them are made to work less than their potential. This kind of underemployment is hidden in contrast to someone who does not have a job and is clearly visible as unemployed. Hence, it is also called disguised unemployment. Now, supposing a landlord, Sukhram, comes and hires one or two members of the family to work on his land. Laxmis family is now able to earn some extra income through wages. Since you do not need five people to look after that small plot, two people moving out does not affect production on their farm. In the above example, two people may move to work in a factory. Once again the earnings of the family would increase and they would also continue to produce as much from their land. There are lakhs of farmers like Laxmi in India. This means that even if we remove a lot of people from agricultural sector and provide them with proper work elsewhere, agricultural production will not suffer. The incomes of the people who take up other work would increase the total family income. This underemployment can also happen in other sectors. For example there are thousands of casual workers in the service sector in urban areas who search for daily employment. They are employed as painters, plumbers, repair persons and others doing odd jobs. Many of them dont find work everyday. Similarly, we see other people of the service sector on the street pushing a cart or selling something where they may spend the whole day but earn very little. 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SCIENCE 4 1.3 States of Matter Observe different types of matter around you. What are its different states? We can see that matter around us exists in three different states solid, liquid and gas. These states of matter arise due to the variation in the characteristics of the particles of matter. Now, let us study about the properties of these three states of matter in detail. 1.3.1 THE SOLID STATE Activity 1.9 Collect the following articles a pen, a book, a needle and a piece of wooden stick. Sketch the shape of the above articles in your notebook by moving a pencil around them. Do all these have a definite shape, distinct boundaries and a fixed volume? What happens if they are hammered, pulled or dropped? Are these capable of diffusing into each other? Try compressing them by applying force. Are you able to compress them? All the above are examples of solids. We can observe that all these have a definite shape, distinct boundaries and fixed volumes, that is, have negligible compressibility. Solids have a tendency to maintain their shape when subjected to outside force. Solids may break under force but it is difficult to change their shape, so they are rigid. Consider the following (a) What about a rubber band, can it change its shape on stretching? Is it a solid? (b) What about sugar and salt? When kept in different jars these take the shape of the jar. Are they solid? (c) What about a sponge? It is a solid yet we are able to compress it. Why? All the above are solids as A rubber band changes shape under force and regains the same shape when the force is removed. If excessive force is applied, it breaks. The shape of each individual sugar or salt crystal remains fixed, whether we take it in our hand, put it in a plate or in a jar. A sponge has minute holes, in which air is trapped, when we press it, the air is expelled out and we are able to compress it. 1.3.2 THE LIQUID STATE Activity 1.10 Collect the following (a) water, cooking oil, milk, juice, a cold drink. (b) containers of different shapes. Put a 50 mL mark on these containers using a measuring cylinder from the laboratory. What will happen if these liquids are spilt on the floor? Measure 50 mL of any one liquid and transfer it into different containers one by one. Does the volume remain the same? Does the shape of the liquid remain the same ? When you pour the liquid from one container into another, does it flow easily? We observe that liquids have no fixed shape but have a fixed volume. They take up the shape of the container in which they are kept. Liquids flow and change shape, so they are not rigid but can be called fluid. Refer to activities 1.4 and 1.5 where we saw that solids and liquids can diffuse into liquids. The gases from the atmosphere diffuse and dissolve in water. These gases, especially oxygen and carbon dioxide, are essential for the survival of aquatic animals and plants. All living creatures need to breathe for survival. The aquatic animals can breathe under water due to the presence of dissolved oxygen in water. Thus, we may conclude that solids, liquids and gases can diffuse into liquids. 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Foreword iii History and a Changing World v Section I Events and Processes 1-74 I. The French Revolution 3 II. Socialism in Europe and the Russian Revolution 25 III. Nazism and the Rise of Hitler 49 Section II Livelihoods, Economies and Societies 75-116 IV. Forest Society and Colonialism 77 V. 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Metals and Non-metals You may have observed the following general properties for ionic compounds (i) Physical nature Ionic compounds are solids and are somewhat hard because of the strong force of attraction between the positive and negative ions. These compounds are generally brittle and break into pieces when pressure is applied. (ii) Melting and Boiling points Ionic compounds have high melting and boiling points (see Table 3.4). This is because a considerable amount of energy is required to break the strong inter-ionic attraction. (iii) Solubility Electrovalent compounds are generally soluble in water and insoluble in solvents such as kerosene, petrol, etc. (iv) Conduction of Electricity The conduction of electricity through a solution involves the movement of charged particles. A solution of an ionic compound in water contains ions, which move to the opposite electrodes when electricity is passed through the solution. Ionic compounds in the solid state do not conduct electricity because movement of ions in the solid is not possible due to their rigid structure. But ionic compounds conduct electricity in the molten state. This is possible in the molten state since the elecrostatic forces of attraction between the oppositely charged ions are overcome due to the heat. Thus, the ions move freely and conduct electricity. 1. (i) Write the electron-dot structures for sodium, oxygen and magnesium. (ii) Show the formation of Na2O and MgO by the transfer of electrons. (iii) What are the ions present in these compounds? 2. Why do ionic compounds have high melting points? The earths crust is the major source of metals. Seawater also contains some soluble salts such as sodium chloride, magnesium chloride, etc. The elements or compounds, which occur naturally in the earths crust, are known as minerals. At some places, minerals contain a very high percentage of a particular metal and the metal can be profitably extracted from it. These minerals are called ores. You have learnt about the reactivity series of metals. Having this knowledge, you can easily understand how a metal is extracted from its ore. Some metals are found in the earths crust in the free state. Some are found in the form of their compounds. The metals at the bottom of the activity series are the least reactive. 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Light Reflection and Refraction Figure 10.16 Figure 10.16 Figure 10.16 Figure 10.16 Figure 10.16 The position, size and the nature of the image formed by a convex lens for various positions of the object Figure 10.17 Figure 10.17 Figure 10.17 Figure 10.17 Figure 10.17 Nature, position and relative size of the image formed by a concave lens For lenses, we follow sign convention, similar to the one used for spherical mirrors. We apply the rules for signs of distances, except that all measurements are taken from the optical centre of the lens. According to the convention, the focal length of a convex lens is positive and that of a concave lens is negative. You must take care to apply appropriate signs for the values of u, v, f, object height h and image height h. As we have a formula for spherical mirrors, we also have formula for spherical lenses. This formula gives the relationship between object- distance (u), image-distance (v) and the focal length (f ). The lens formula is expressed as 1 1 1 v u f (10.8) The lens formula given above is general and is valid in all situations for any spherical lens. 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PAIR OF LINEAR EQUATIONS IN TWO VARIABLES 57 2. Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method (i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1 2 if we only add 1 to the denominator. What is the fraction? (ii) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu? (iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number. (iv) Meena went to a bank to withdraw 2000. She asked the cashier to give her 50 and 100 notes only. Meena got 25 notes in all. Find how many notes of 50 and 100 she received. (v) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid 27 for a book kept for seven days, while Susy paid 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day. 3.4.3 Cross - Multiplication Method So far, you have learnt how to solve a pair of linear equations in two variables by graphical, substitution and elimination methods. Here, we introduce one more algebraic method to solve a pair of linear equations which for many reasons is a very useful method of solving these equations. Before we proceed further, let us consider the following situation. The cost of 5 oranges and 3 apples is 35 and the cost of 2 oranges and 4 apples is 28. Let us find the cost of an orange and an apple. Let us denote the cost of an orange by x and the cost of an apple by y. Then, the equations formed are 5x 3y 35, i.e., 5x 3y 35 0 (1) 2x 4y 28, i.e., 2x 4y 28 0 (2) Let us use the elimination method to solve these equations. Multiply Equation (1) by 4 and Equation (2) by 3. We get (4)(5)x (4)(3)y (4)(35) 0 (3) (3)(2)x (3)(4)y (3)(28) 0 (4) Subtracting Equation (4) from Equation (3), we get (5)(4) (3)(2)x (4)(3) (3)(4)y 4(35) (3)(28) 0 2019-20	[ 82966, 3008, 30851, 934, 468, 5757, 21792, 1964, 46258, 76753, 220, 20, 22, 220, 17, 13, 3377, 279, 6716, 315, 13482, 37906, 304, 279, 2701, 5322, 11, 323, 1477, 862, 9904, 320, 333, 807, 3000, 8, 553, 279, 42932, 1714, 320, 72, 8, 1416, 582, 912, 220, 16, 311, 279, 63533, 323, 32256, 220, 16, 504, 279, 46912, 11, 264, 19419, 25271, 311, 220, 16, 13, 1084, 9044, 220, 16, 220, 17, 421, 582, 1172, 912, 220, 16, 311, 279, 46912, 13, 3555, 374, 279, 19419, 30, 320, 3808, 8, 20924, 1635, 4134, 11, 451, 6070, 572, 8807, 558, 438, 2310, 438, 11840, 84, 13, 17695, 1635, 2937, 11, 451, 6070, 686, 387, 10917, 438, 2310, 438, 11840, 84, 13, 2585, 2310, 525, 451, 6070, 323, 11840, 84, 30, 320, 34594, 8, 576, 2629, 315, 279, 18509, 315, 264, 1378, 48342, 1372, 374, 220, 24, 13, 7281, 11, 11627, 3039, 419, 1372, 374, 10917, 279, 1372, 12180, 553, 75183, 279, 1973, 315, 279, 18509, 13, 7379, 279, 1372, 13, 320, 344, 8, 2157, 7157, 3937, 311, 264, 6073, 311, 14798, 220, 17, 15, 15, 15, 13, 2932, 4588, 279, 90355, 311, 2968, 1059, 220, 20, 15, 323, 220, 16, 15, 15, 8388, 1172, 13, 2157, 7157, 2684, 220, 17, 20, 8388, 304, 678, 13, 7379, 1246, 1657, 8388, 315, 220, 20, 15, 323, 220, 16, 15, 15, 1340, 3949, 13, 320, 85, 8, 362, 39551, 6733, 702, 264, 8356, 6757, 369, 279, 1156, 2326, 2849, 323, 458, 5107, 6757, 369, 1817, 1899, 44995, 13, 13637, 410, 64, 7171, 220, 17, 22, 369, 264, 2311, 8604, 369, 8094, 2849, 11, 1393, 16288, 88, 7171, 220, 17, 16, 369, 279, 2311, 1340, 8604, 369, 4236, 2849, 13, 7379, 279, 8356, 6757, 323, 279, 6757, 369, 1817, 4960, 1899, 13, 220, 18, 13, 19, 13, 18, 11261, 481, 58712, 1693, 6730, 2055, 3041, 11, 498, 614, 49250, 1246, 311, 11625, 264, 6716, 315, 13482, 37906, 304, 1378, 7332, 553, 53143, 11, 48968, 323, 42932, 5413, 13, 5692, 11, 582, 19131, 825, 803, 46876, 292, 1714, 311, 11625, 264, 6716, 315, 13482, 37906, 892, 369, 1657, 7966, 374, 264, 1602, 5390, 1714, 315, 21828, 1493, 37906, 13, 13235, 582, 10354, 4623, 11, 1077, 601, 2908, 279, 2701, 6534, 13, 576, 2783, 315, 220, 20, 84038, 323, 220, 18, 40676, 374, 220, 18, 20, 323, 279, 2783, 315, 220, 17, 84038, 323, 220, 19, 40676, 374, 220, 17, 23, 13, 6771, 601, 1477, 279, 2783, 315, 458, 18575, 323, 458, 23268, 13, 6771, 601, 78064, 279, 2783, 315, 458, 18575, 553, 856, 323, 279, 2783, 315, 458, 23268, 553, 379, 13, 5005, 11, 279, 37906, 14122, 525, 220, 20, 87, 220, 18, 88, 220, 18, 20, 11, 600, 1734, 2572, 220, 20, 87, 220, 18, 88, 220, 18, 20, 220, 15, 320, 16, 8, 220, 17, 87, 220, 19, 88, 220, 17, 23, 11, 600, 1734, 2572, 220, 17, 87, 220, 19, 88, 220, 17, 23, 220, 15, 320, 17, 8, 6771, 601, 990, 279, 42932, 1714, 311, 11625, 1493, 37906, 13, 71059, 84670, 320, 16, 8 ]	[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
TRIANGLES 113 See that these two triangles are not congruent. Repeat this activity with some more pairs of triangles. So, equality of one pair of sides or one pair of sides and one pair of angles is not sufficient to give us congruent triangles. What would happen if the other pair of arms (sides) of the equal angles are also equal? In Fig 7.7, BC QR, B Q and also, AB PQ. Now, what can you say about congruence of ABC and PQR? Recall from your earlier classes that, in this case, the two triangles are congruent. Verify this for ABC and PQR in Fig. 7.7. Repeat this activity with other pairs of triangles. Do you observe that the equality of two sides and the included angle is enough for the congruence of triangles? Yes, it is enough. Fig. 7.7 This is the first criterion for congruence of triangles. Axiom 7.1 (SAS congruence rule) Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle. This result cannot be proved with the help of previously known results and so it is accepted true as an axiom (see Appendix 1). Let us now take some examples. Example 1 In Fig. 7.8, OA OB and OD OC. Show that (i) AOD BOC and (ii) AD BC. Solution (i) You may observe that in AOD and BOC, OA OB (Given) OD OC Fig. 7.8 2019-2020	[ 2378, 40, 74753, 220, 16, 16, 18, 3496, 429, 1493, 1378, 42446, 525, 537, 30169, 11680, 13, 44801, 419, 5702, 448, 1045, 803, 13530, 315, 42446, 13, 2055, 11, 21777, 315, 825, 6716, 315, 11067, 476, 825, 6716, 315, 11067, 323, 825, 6716, 315, 25941, 374, 537, 14016, 311, 2968, 601, 30169, 11680, 42446, 13, 3555, 1035, 3537, 421, 279, 1008, 6716, 315, 11715, 320, 82, 3341, 8, 315, 279, 6144, 25941, 525, 1083, 6144, 30, 758, 23095, 220, 22, 13, 22, 11, 18040, 38699, 11, 425, 1207, 323, 1083, 11, 14137, 61717, 13, 4695, 11, 1128, 646, 498, 1977, 911, 30169, 84, 763, 315, 19360, 323, 393, 30465, 30, 79540, 504, 697, 6788, 6846, 429, 11, 304, 419, 1142, 11, 279, 1378, 42446, 525, 30169, 11680, 13, 25429, 419, 369, 19360, 323, 393, 30465, 304, 23095, 13, 220, 22, 13, 22, 13, 44801, 419, 5702, 448, 1008, 13530, 315, 42446, 13, 3155, 498, 22986, 429, 279, 21777, 315, 1378, 11067, 323, 279, 5230, 9210, 374, 3322, 369, 279, 30169, 84, 763, 315, 42446, 30, 7414, 11, 432, 374, 3322, 13, 23095, 13, 220, 22, 13, 22, 1096, 374, 279, 1156, 35957, 369, 30169, 84, 763, 315, 42446, 13, 362, 11665, 316, 220, 22, 13, 16, 320, 50, 1911, 30169, 84, 763, 5912, 8, 9043, 42446, 525, 30169, 11680, 421, 1378, 11067, 323, 279, 5230, 9210, 315, 825, 21495, 525, 6144, 311, 279, 1378, 11067, 323, 279, 5230, 9210, 315, 279, 1008, 21495, 13, 1096, 1102, 4157, 387, 18651, 448, 279, 1492, 315, 8597, 3881, 3059, 323, 773, 432, 374, 11666, 830, 438, 458, 88177, 320, 4060, 64714, 220, 16, 568, 6771, 601, 1431, 1896, 1045, 10295, 13, 13383, 220, 16, 758, 23095, 13, 220, 22, 13, 23, 11, 80442, 43173, 323, 52732, 31867, 13, 6928, 429, 320, 72, 8, 362, 2069, 425, 7612, 323, 320, 3808, 8, 9630, 18040, 13, 12478, 320, 72, 8, 1446, 1231, 22986, 429, 304, 362, 2069, 323, 425, 7612, 11, 80442, 43173, 320, 22043, 8, 52732, 31867, 23095, 13, 220, 22, 13, 23, 220, 17, 15, 16, 24, 12, 17, 15, 17, 15, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645 ]	[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
72 DEMOCRATIC POLITICS 4 Which of the following institutions can make changes to an existing law of the country? a The Supreme Court b The President c The Prime Minister d The Parliament 5 Match the ministry with the news that the ministry may have released exercises a A new policy is being made to increase the jute exports from the country. b Telephone services will be made more accessible to rural areas. c The price of rice and wheat sold under the Public Distribution System will go down. d A pulse polio campaign will be launched. e The allowances of the soldiers posted on high altitudes will be increased. i Ministry of Defence ii Ministry of Agriculture, Food and Public Distribution iii Ministry of Health iv Ministry of Commerce and Industry v Ministry of Communications and Information Technology 6 Of all the institutions that we have studied in this chapter, name the one that exercises the powers on each of the following matters. a Decision on allocation of money for developing infrastructure like roads, irrigation etc. and different welfare activities for the citizens b Considers the recommendation of a Committee on a law to regulate the stock exchange c Decides on a legal dispute between two state governments d Implements the decision to provide relief for the victims of an earthquake. 7 Why is the Prime Minister in India not directly elected by the people? Choose the most appropriate answer and give reasons for your choice. a In a Parliamentary democracy only the leader of the majority party in the Lok Sabha can become the Prime Minister. b Lok Sabha can remove the Prime Minister and the Council of Ministers even before the expiry of their term. c Since the Prime Minister is appointed by the President there is no need for it. d Direct election of the Prime Minister will involve lot of expenditure on election. 8 Three friends went to watch a film that showed the hero becoming Chief Minister for a day and making big changes in the state. Imran said this is what the country needs. 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Until the middle of the twentieth century, production was largely organised within countries. What crossed the boundaries of these countries were raw material, food stuff and finished products. Colonies such as India exported raw materials and food stuff and imported finished goods. Trade was the main channel connecting distant countries. This was before large companies called A large MNC, producing industrial equipment, designs its products in research centres in the United States, and then has the components manufactured in China. These are then shipped to Mexico and Eastern Europe where the products are assembled and the finished products are sold all over the world. Meanwhile, the companys customer care is carried out through call centres located in India. multinational corporations (MNCs) emerged on the scene. A MNC is a company that owns or controls production in more than one nation. MNCs set up offices and factories for production in regions where they can get cheap labour and other resources. This is done so that the cost of production is low and the MNCs can earn greater profits. Consider the following example. 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SCIENCE 166 pleasant is said to be of a rich quality. A sound of single frequency is called a tone. The sound which is produced due to a mixture of several frequencies is called a note and is pleasant to listen to. Noise is unpleasant to the ear! Music is pleasant to hear and is of rich quality. uestions 1. Which wave property determines (a) loudness, (b) pitch? 2. Guess which sound has a higher pitch guitar or car horn? The speed of sound is defined as the distance which a point on a wave, such as a compression or a rarefaction, travels per unit time. We know, speed, v distance time T Here is the wavelength of the sound wave. It is the distance travelled by the sound wave in one time period (T) of the wave. Thus, v or v That is, speed wavelength frequency. The speed of sound remains almost the same for all frequencies in a given medium under the same physical conditions. Example 12.1 A sound wave has a frequency of 2 kHz and wave length 35 cm. How long will it take to travel 1.5 km? Solution Given, Frequency, 2 kHz 2000 Hz Wavelength, 35 cm 0.35 m We know that speed, v of the wave wavelength frequency v 0.35 m 2000 Hz 700 ms The time taken by the wave to travel a distance, d of 1.5 km is Thus sound will take 2.1 s to travel a distance of 1.5 km. uestions 1. What are wavelength, frequency, time period and amplitude of a sound wave? 2. How are the wavelength and frequency of a sound wave related to its speed? 3. Calculate the wavelength of a sound wave whose frequency is 220 Hz and speed is 440 ms in a given medium. 4. A person is listening to a tone of 500 Hz sitting at a distance of 450 m from the source of the sound. What is the time interval between successive compressions from the source? The amount of sound energy passing each second through unit area is called the intensity of sound. We sometimes use the terms loudness and intensity interchangeably, but they are not the same. Loudness is a measure of the response of the ear to the sound. Even when two sounds are of equal intensity, we may hear one as louder than the other simply because our ear detects it better. uestion 1. Distinguish between loudness and intensity of sound. 12.2.4 SPEED OF SOUND IN DIFFERENT MEDIA Sound propagates through a medium at a finite speed. The sound of a thunder is heard a little later than the flash of light is seen. Q Q Q 2019-2020	[ 3540, 56682, 220, 16, 21, 21, 23795, 374, 1053, 311, 387, 315, 264, 9080, 4271, 13, 362, 5112, 315, 3175, 11639, 374, 2598, 264, 16232, 13, 576, 5112, 892, 374, 8947, 4152, 311, 264, 20980, 315, 3807, 33773, 374, 2598, 264, 5185, 323, 374, 23795, 311, 8844, 311, 13, 50523, 374, 46889, 311, 279, 2430, 0, 10717, 374, 23795, 311, 6723, 323, 374, 315, 9080, 4271, 13, 220, 3045, 908, 220, 16, 13, 15920, 12060, 3343, 26569, 320, 64, 8, 17361, 2090, 11, 320, 65, 8, 9649, 30, 220, 17, 13, 54279, 892, 5112, 702, 264, 5080, 9649, 16986, 476, 1803, 20631, 30, 576, 4628, 315, 5112, 374, 4512, 438, 279, 6010, 892, 264, 1459, 389, 264, 12060, 11, 1741, 438, 264, 25111, 476, 264, 8848, 90309, 11, 34192, 817, 4982, 882, 13, 1205, 1414, 11, 4628, 11, 348, 6010, 882, 350, 5692, 374, 279, 45306, 315, 279, 5112, 12060, 13, 1084, 374, 279, 6010, 45268, 553, 279, 5112, 12060, 304, 825, 882, 4168, 320, 51, 8, 315, 279, 12060, 13, 14301, 11, 348, 476, 348, 2938, 374, 11, 4628, 45306, 11639, 13, 576, 4628, 315, 5112, 8458, 4558, 279, 1852, 369, 678, 33773, 304, 264, 2661, 11051, 1212, 279, 1852, 6961, 4682, 13, 13383, 220, 16, 17, 13, 16, 362, 5112, 12060, 702, 264, 11639, 315, 220, 17, 69626, 323, 12060, 3084, 220, 18, 20, 9961, 13, 2585, 1293, 686, 432, 1896, 311, 5821, 220, 16, 13, 20, 13136, 30, 12478, 16246, 11, 42380, 11, 220, 17, 69626, 220, 17, 15, 15, 15, 36092, 467, 34861, 11, 220, 18, 20, 9961, 220, 15, 13, 18, 20, 296, 1205, 1414, 429, 4628, 11, 348, 315, 279, 12060, 45306, 11639, 348, 220, 15, 13, 18, 20, 296, 220, 17, 15, 15, 15, 36092, 220, 22, 15, 15, 9829, 576, 882, 4429, 553, 279, 12060, 311, 5821, 264, 6010, 11, 294, 315, 220, 16, 13, 20, 13136, 374, 14301, 5112, 686, 1896, 220, 17, 13, 16, 274, 311, 5821, 264, 6010, 315, 220, 16, 13, 20, 13136, 13, 220, 3045, 908, 220, 16, 13, 3555, 525, 45306, 11, 11639, 11, 882, 4168, 323, 44109, 315, 264, 5112, 12060, 30, 220, 17, 13, 2585, 525, 279, 45306, 323, 11639, 315, 264, 5112, 12060, 5435, 311, 1181, 4628, 30, 220, 18, 13, 20517, 279, 45306, 315, 264, 5112, 12060, 6693, 11639, 374, 220, 17, 17, 15, 36092, 323, 4628, 374, 220, 19, 19, 15, 9829, 304, 264, 2661, 11051, 13, 220, 19, 13, 362, 1697, 374, 14289, 311, 264, 16232, 315, 220, 20, 15, 15, 36092, 11699, 518, 264, 6010, 315, 220, 19, 20, 15, 296, 504, 279, 2530, 315, 279, 5112, 13, 3555, 374, 279, 882, 9873, 1948, 48924, 24611, 908, 504, 279, 2530, 30, 576, 3311, 315, 5112, 4802, 12299, 1817, 2086, 1526, 4982, 3082, 374, 2598, 279, 20612, 315, 5112, 13, 1205, 7025, 990, 279, 3793, 17361, 2090, 323, 20612, 51263, 2845, 11, 714, 807, 525, 537, 279, 1852, 13, 79548, 2090, 374, 264, 6629, 315, 279, 2033, 315, 279, 2430, 311, 279, 5112, 13, 7418, 979, 1378, 10362, 525, 315, 6144, 20612 ]	[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
SCIENCE 200 14.4.4 THE OXYGEN-CYCLE Oxygen is a very abundant element on our Earth. It is found in the elemental form in the atmosphere to the extent of 21. It also occurs extensively in the combined form in the Earths crust as well as also in the air in the form of carbon dioxide. In the crust, it is found as the oxides of most metals and silicon, and also as carbonate, sulphate, nitrate and other minerals. It is also an essential component of most biological molecules like carbohydrates, proteins, nucleic acids and fats (or lipids). But when we talk of the oxygen-cycle, we are mainly referring to the cycle that maintains the levels of oxygen in the atmosphere. Oxygen from the atmosphere is used up in three processes, namely combustion, respiration and in the formation of oxides of nitrogen. Oxygen is returned to the atmosphere in only one major process, that is, photosynthesis. And this forms the broad outline of the oxygen-cycle in nature (Fig. 14.8). bacteria, are poisoned by elemental oxygen. In fact, even the process of nitrogen-fixing by bacteria does not take place in the presence of oxygen. 14.5 Ozone Layer Elemental oxygen is normally found in the form of a diatomic molecule. However, in the upper reaches of the atmosphere, a molecule containing three atoms of oxygen is found. This would mean a formula of O3 and this is called ozone. Unlike the normal diatomic molecule of oxygen, ozone is poisonous and we are lucky that it is not stable nearer to the Earths surface. But it performs an essential function where it is found. It absorbs harmful radiations from the Sun. This prevents those harmful radiations from reaching the surface of the Earth where they may damage many forms of life. Recently it was discovered that this ozone layer was getting depleted. Various man-made compounds like CFCs (carbon compounds having both fluorine and chlorine which are very stable and not degraded by any biological process) were found to persist in the atmosphere. Once they reached the ozone layer, they would react with the ozone molecules. This resulted in a reduction of the ozone layer and recently they have discovered a hole in the ozone layer above the Antartica. It is difficult to imagine the consequences for life on Earth if the ozone layer dwindles further, but many people think that it would be better not to take chances. These people advocate working towards stopping all further damage to the ozone layer. Fig. 14.8 Oxygen-cycle in nature Though we usually think of oxygen as being necessary to life in the process of respiration, it might be of interest to you to learn that some forms of life, especially Fig. 14.9 Satellite picture showing the hole (magenta colour) in the ozone layer over Antartica October 1980 October 1985 October 1990 2019-2020	[ 3540, 56682, 220, 17, 15, 15, 220, 16, 19, 13, 19, 13, 19, 3168, 506, 16356, 11085, 7658, 56, 29401, 86569, 374, 264, 1602, 43511, 2392, 389, 1039, 9237, 13, 1084, 374, 1730, 304, 279, 61135, 1352, 304, 279, 16566, 311, 279, 12818, 315, 220, 17, 16, 13, 1084, 1083, 13666, 41717, 304, 279, 10856, 1352, 304, 279, 9237, 82, 39612, 438, 1632, 438, 1083, 304, 279, 3720, 304, 279, 1352, 315, 12499, 39489, 13, 758, 279, 39612, 11, 432, 374, 1730, 438, 279, 18952, 3341, 315, 1429, 36082, 323, 50592, 11, 323, 1083, 438, 83343, 11, 82678, 349, 11, 24691, 7698, 323, 1008, 32972, 13, 1084, 374, 1083, 458, 7565, 3692, 315, 1429, 23275, 34615, 1075, 61245, 11, 27796, 11, 30384, 292, 32869, 323, 49027, 320, 269, 19050, 3365, 568, 1988, 979, 582, 3061, 315, 279, 23552, 77690, 11, 582, 525, 14576, 22023, 311, 279, 10775, 429, 31995, 279, 5866, 315, 23552, 304, 279, 16566, 13, 86569, 504, 279, 16566, 374, 1483, 705, 304, 2326, 11364, 11, 31025, 58233, 11, 592, 28479, 323, 304, 279, 18003, 315, 18952, 3341, 315, 46403, 13, 86569, 374, 5927, 311, 279, 16566, 304, 1172, 825, 3598, 1882, 11, 429, 374, 11, 7249, 73667, 13, 1597, 419, 7586, 279, 7205, 21101, 315, 279, 23552, 77690, 304, 6993, 320, 28935, 13, 220, 16, 19, 13, 23, 568, 23157, 11, 525, 70498, 553, 61135, 23552, 13, 758, 2097, 11, 1496, 279, 1882, 315, 46403, 70913, 287, 553, 23157, 1558, 537, 1896, 1992, 304, 279, 9362, 315, 23552, 13, 220, 16, 19, 13, 20, 506, 8684, 22735, 70638, 23552, 374, 14279, 1730, 304, 279, 1352, 315, 264, 1853, 6618, 41930, 13, 4354, 11, 304, 279, 8416, 24491, 315, 279, 16566, 11, 264, 41930, 8482, 2326, 32199, 315, 23552, 374, 1730, 13, 1096, 1035, 3076, 264, 14806, 315, 506, 18, 323, 419, 374, 2598, 76437, 13, 26048, 279, 4622, 1853, 6618, 41930, 315, 23552, 11, 76437, 374, 73408, 323, 582, 525, 17605, 429, 432, 374, 537, 15175, 86820, 311, 279, 9237, 82, 7329, 13, 1988, 432, 26674, 458, 7565, 729, 1380, 432, 374, 1730, 13, 1084, 90011, 27756, 11900, 804, 504, 279, 8059, 13, 1096, 27934, 1846, 27756, 11900, 804, 504, 18739, 279, 7329, 315, 279, 9237, 1380, 807, 1231, 5557, 1657, 7586, 315, 2272, 13, 40996, 432, 572, 11105, 429, 419, 76437, 6193, 572, 3709, 78166, 13, 39641, 883, 26877, 31146, 1075, 356, 6754, 82, 320, 73341, 31146, 3432, 2176, 53636, 482, 323, 84106, 892, 525, 1602, 15175, 323, 537, 90878, 553, 894, 23275, 1882, 8, 1033, 1730, 311, 22334, 304, 279, 16566, 13, 9646, 807, 8643, 279, 76437, 6193, 11, 807, 1035, 13767, 448, 279, 76437, 34615, 13, 1096, 19006, 304, 264, 13951, 315, 279, 76437, 6193, 323, 5926, 807, 614, 11105, 264, 14178, 304, 279, 76437, 6193, 3403, 279, 6755, 471, 3001, 13, 1084, 374, 5000, 311, 12793, 279, 15917, 369, 2272, 389, 9237, 421, 279, 76437, 6193, 82122, 642, 4623, 11, 714, 1657, 1251, 1744, 429, 432, 1035, 387, 2664, 537, 311, 1896, 16963, 13, 4220, 1251, 28015, 3238, 6974, 22535, 678, 4623, 5557, 311, 279 ]	[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
326 MATHEMATICS EXERCISE 1.3 1. (i) 0.36, terminating. (ii) 0.09 , non-terminating repeating. (iii) 4.125, terminating. (iv) 0.230769 , non-terminating repeating. (v) 0.18 non-terminating repeating. (vi) 0.8225 terminating. 2. 2 1 2 0.285714, 7 7 3 1 3 0.428571, 7 7 4 1 4 0.571428, 7 7 5 1 5 0.714285, 7 7 6 1 6 0.857142 7 7 3. (i) 2 3 Let x 0.666. . . So 10x 6.666. . . or, 10x 6 x or , x 6 2 9 3 (ii) 43 90 (iii) 1 999 4. 1 Let x 0.9999. . . So 10 x 9.999. . . or, 10 x 9 x or, x 1 5. 0.0588235294117647 6. The prime factorisation of q has only powers of 2 or powers of 5 or both. 7. 0.01001000100001. . ., 0.202002000200002. . ., 0.003000300003. . . 8. 0.75075007500075000075. . ., 0.767076700767000767. . ., 0.808008000800008. . . 9. (i) and (v) irrational (ii), (iii) and (iv) rational. EXERCISE 1.4 1. Proceed as in Section 1.4 for 2.665. 2. Proceed as in Example 11. EXERCISE 1.5 1. (i) Irrational (ii) Rational (iii) Rational (iv) Irrational (v) Irrational 2. (i) 6 3 2 2 3 6 (ii) 6 (iii) 7 2 10 (iv) 3 3. There is no contradiction. Remember that when you measure a length with a scale or any other device, you only get an approximate rational value. 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Sustainable Management of Natural Resources Lastly, we come to the nature and wildlife enthusiasts who are in no way dependent on the forests, but who may have considerable say in their management. The conservationists were initially taken up with large animals like lions, tigers, elephants and rhinoceros. They now recognise the need to preserve biodiversity as a whole. But shouldnt we recognise people as forming part of the forest system? There have been enough instances of local people working traditionally for conservation of forests. For example, the case of Bishnois community living in western Rajasthan on the border of the Thar desert. Conservation of forest and wildlife has been a religious tenet for them. These nature-loving people have for centuries, been conserving the flora and fauna to the extent of sacrificing their lives to protect the environment. They are living with the basic philosophy that all living things have a right to survive and share all resources. The Government of India has recently instituted an Amrita Devi Bishnoi National Award for Wildlife Conservation in the memory of Amrita Devi Bishnoi, who in 1731 sacrificed her life along with 363 others for the protection of khejri trees in Khejrali village near Jodhpur in Rajasthan. Studies have shown that the prejudice against the traditional use of forest areas has no basis. Here is an example the great Himalayan National Park contains, within its reserved area, alpine meadows which were grazed by sheep in summer. Nomadic shepherds drove their flock up from the valleys every summer. When this national park was formed, this practice was put to an end. Now it is seen that without the regular grazing by sheep the grass first grows very tall, and then falls over preventing fresh growth. Management of protected areas by keeping the local people out or by using force cannot possibly be successful in the long run. In any case, the damage caused to forests cannot be attributed to only the local people one cannot turn a blind eye to the deforestation caused by industrial needs or development projects like building roads or dams. The damage caused in these reserves by tourists or the arrangements made for their convenience is also to be considered. We need to accept that human intervention has been very much a part of the forest landscape. What has to be managed in the nature and what may be the extent of this intervention? Forest resources ought to be used in a manner that is both environmentally and developmentally sound in other words, while the environment is preserved, the benefits of the controlled exploitation go to the local people, a process in which decentralised economic growth and ecological conservation go hand in hand. The kind of economic and social development we want will ultimately determine whether the environment will be conserved or further destroyed. The environment must not be regarded as a pristine collection of plants and animals. It is a vast and complex entity that offers a range of natural resources for our use. We need to use these resources with due caution for our economic and social growth, and to meet our material aspirations. 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18 MATHEMATICS 2. Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions. 3. The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form , p q what can you say about the prime factors of q? (i) 43.123456789 (ii) 0.120120012000120000. . . (iii) 43.123456789 1.6 Summary In this chapter, you have studied the following points 1. Euclids division lemma Given positive integers a and b, there exist whole numbers q and r satisfying a bq r, 0 r b. 2. Euclids division algorithm This is based on Euclids division lemma. According to this, the HCF of any two positive integers a and b, with a b, is obtained as follows Step 1 Apply the division lemma to find q and r where a bq r, 0 r b. Step 2 If r 0, the HCF is b. If r 0, apply Euclids lemma to b and r. Step 3 Continue the process till the remainder is zero. The divisor at this stage will be HCF (a, b). Also, HCF(a, b) HCF(b, r). 3. The Fundamental Theorem of Arithmetic Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur. 4. If p is a prime and p divides a2, then p divides a, where a is a positive integer. 5. To prove that 2, 3 are irrationals. 6. Let x be a rational number whose decimal expansion terminates. Then we can express x in the form p q , where p and q are coprime, and the prime factorisation of q is of the form 2n5m, where n, m are non-negative integers. 7. Let x p q be a rational number, such that the prime factorisation of q is of the form 2n5m, where n, m are non-negative integers. Then x has a decimal expansion which terminates. 8. Let x p q be a rational number, such that the prime factorisation of q is not of the form 2n 5m, where n, m are non-negative integers. 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234 MATHEMATICS Example 6 Find the area of the shaded design in Fig. 12.17, where ABCD is a square of side 10 cm and semicircles are drawn with each side of the square as diameter. (Use 3.14) Fig. 12.17 Fig. 12.18 Solution Let us mark the four unshaded regions as I, II, III and IV (see Fig. 12.18). Area of I Area of III Area of ABCD Areas of two semicircles of each of radius 5 cm 2 2 1 10 10 2 5 cm 2 (100 3.14 25) cm2 (100 78.5) cm2 21.5 cm2 Similarly, Area of II Area of IV 21.5 cm2 So, area of the shaded design Area of ABCD Area of (I II III IV) (100 2 21.5) cm2 (100 43) cm2 57 cm2 EXERCISE 12.3 Unless stated otherwise, use 22 7 1. Find the area of the shaded region in Fig. 12.19, if PQ 24 cm, PR 7 cm and O is the centre of the circle. 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NUMBER SYSTEMS 5 EXERCISE 1.1 1. Is zero a rational number? Can you write it in the form p q , where p and q are integers and q 0? 2. Find six rational numbers between 3 and 4. 3. Find five rational numbers between 3 5 and 4 5 . 4. State whether the following statements are true or false. Give reasons for your answers. (i) Every natural number is a whole number. (ii) Every integer is a whole number. (iii) Every rational number is a whole number. 1.2 Irrational Numbers We saw, in the previous section, that there may be numbers on the number line that are not rationals. In this section, we are going to investigate these numbers. So far, all the numbers you have come across, are of the form p q , where p and q are integers and q 0. So, you may ask are there numbers which are not of this form? There are indeed such numbers. The Pythagoreans in Greece, followers of the famous mathematician and philosopher Pythagoras, were the first to discover the numbers which were not rationals, around 400 BC. These numbers are called irrational numbers (irrationals), because they cannot be written in the form of a ratio of integers. There are many myths surrounding the discovery of irrational numbers by the Pythagorean, Hippacus of Croton. In all the myths, Hippacus has an unfortunate end, either for discovering that 2 is irrational or for disclosing the secret about 2 to people outside the secret Pythagorean sect! Let us formally define these numbers. A number s is called irrational, if it cannot be written in the form p q , where p and q are integers and q 0. 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ATOMS AND MOLECULES 41 molecules, ions or particles) is that quantity in number having a mass equal to its atomic or molecular mass in grams. The number of particles (atoms, molecules or ions) present in 1 mole of any substance is fixed, with a value of 6.022 1023. This is an experimentally obtained value. This number is called the Avogadro Constant or Avogadro Number (represented by N0), named in honour of the Italian scientist, Amedeo Avogadro. 1 mole (of anything) 6.022 1023 in number, as, 1 dozen 12 nos. 1 gross 144 nos. Besides being related to a number, a mole has one more advantage over a dozen or a gross. This advantage is that mass of 1 mole of a particular substance is also fixed. The mass of 1 mole of a substance is equal to its relative atomic or molecular mass in grams. The atomic mass of an element gives us the mass of one atom of that element in atomic mass units (u). To get the mass of 1 mole of atom of that element, that is, molar mass, we have to take the same numerical value but change the units from u to g. Molar mass of atoms is also known as gram atomic mass. For example, atomic mass of hydrogen1u. So, gram atomic mass of hydrogen 1 g. 1 u hydrogen has only 1 atom of hydrogen 1 g hydrogen has 1 mole atoms, that is, 6.022 1023 atoms of hydrogen. Similarly, 16 u oxygen has only 1 atom of oxygen, 16 g oxygen has 1 mole atoms, that is, 6.022 1023 atoms of oxygen. To find the gram molecular mass or molar mass of a molecule, we keep the numerical value the same as the molecular mass, but simply change units as above from u to g. For example, as we have already calculated, molecular mass of water (H2O) is 18 u. From here we understand that 18 u water has only 1 molecule of water, 18 g water has 1 mole molecules of water, that is, 6.022 1023 molecules of water. Chemists need the number of atoms and molecules while carrying out reactions, and for this they need to relate the mass in grams to the number. It is done as follows 1 mole 6.022 1023 number Relative mass in grams. Thus, a mole is the chemists counting unit. The word mole was introduced around 1896 by Wilhelm Ostwald who derived the term from the Latin word moles meaning a heap or pile. A substance may be considered as a heap of atoms or molecules. The unit mole was accepted in 1967 to provide a simple way of reporting a large number the massive heap of atoms and molecules in a sample. Example 3.3 1. Calculate the number of moles for the following (i) 52 g of He (finding mole from mass) (ii) 12.044 1023 number of He atoms (finding mole from number of particles). Solutions No. of moles n Given mass m Molar mass M Given number of particles N Avogadro number of particles N0 (i) Atomic mass of He 4 u Molar mass of He 4g Thus, the number of moles given mass molar mass n m M 52 4 13 (ii) we know, 1 mole 6.022 1023 The number of moles given number of particles Avogadro number n N No 12 044 10 6 022 10 2 23 23 . . 2019-2020	[ 77932, 50, 3567, 11418, 84130, 7717, 50, 220, 19, 16, 34615, 11, 64025, 476, 18730, 8, 374, 429, 12194, 304, 1372, 3432, 264, 3072, 6144, 311, 1181, 24510, 476, 30106, 3072, 304, 33319, 13, 576, 1372, 315, 18730, 320, 65550, 11, 34615, 476, 64025, 8, 3042, 304, 220, 16, 34651, 315, 894, 19699, 374, 8356, 11, 448, 264, 897, 315, 220, 21, 13, 15, 17, 17, 220, 16, 15, 17, 18, 13, 1096, 374, 458, 9342, 745, 12180, 897, 13, 1096, 1372, 374, 2598, 279, 7519, 538, 89676, 19305, 476, 7519, 538, 89676, 5624, 320, 52759, 553, 451, 15, 701, 6941, 304, 33562, 315, 279, 14811, 27468, 11, 362, 2061, 24612, 7519, 538, 89676, 13, 220, 16, 34651, 320, 1055, 4113, 8, 220, 21, 13, 15, 17, 17, 220, 16, 15, 17, 18, 304, 1372, 11, 438, 11, 220, 16, 20403, 220, 16, 17, 11891, 13, 220, 16, 19952, 220, 16, 19, 19, 11891, 13, 30809, 1660, 5435, 311, 264, 1372, 11, 264, 34651, 702, 825, 803, 9423, 916, 264, 20403, 476, 264, 19952, 13, 1096, 9423, 374, 429, 3072, 315, 220, 16, 34651, 315, 264, 3953, 19699, 374, 1083, 8356, 13, 576, 3072, 315, 220, 16, 34651, 315, 264, 19699, 374, 6144, 311, 1181, 8674, 24510, 476, 30106, 3072, 304, 33319, 13, 576, 24510, 3072, 315, 458, 2392, 6696, 601, 279, 3072, 315, 825, 19124, 315, 429, 2392, 304, 24510, 3072, 8153, 320, 84, 568, 2014, 633, 279, 3072, 315, 220, 16, 34651, 315, 19124, 315, 429, 2392, 11, 429, 374, 11, 296, 7417, 3072, 11, 582, 614, 311, 1896, 279, 1852, 34776, 897, 714, 2297, 279, 8153, 504, 575, 311, 342, 13, 386, 7417, 3072, 315, 32199, 374, 1083, 3881, 438, 23018, 24510, 3072, 13, 1752, 3110, 11, 24510, 3072, 315, 34684, 16, 84, 13, 2055, 11, 23018, 24510, 3072, 315, 34684, 220, 16, 342, 13, 220, 16, 575, 34684, 702, 1172, 220, 16, 19124, 315, 34684, 220, 16, 342, 34684, 702, 220, 16, 34651, 32199, 11, 429, 374, 11, 220, 21, 13, 15, 17, 17, 220, 16, 15, 17, 18, 32199, 315, 34684, 13, 34239, 11, 220, 16, 21, 575, 23552, 702, 1172, 220, 16, 19124, 315, 23552, 11, 220, 16, 21, 342, 23552, 702, 220, 16, 34651, 32199, 11, 429, 374, 11, 220, 21, 13, 15, 17, 17, 220, 16, 15, 17, 18, 32199, 315, 23552, 13, 2014, 1477, 279, 23018, 30106, 3072, 476, 296, 7417, 3072, 315, 264, 41930, 11, 582, 2506, 279, 34776, 897, 279, 1852, 438, 279, 30106, 3072, 11, 714, 4936, 2297, 8153, 438, 3403, 504, 575, 311, 342, 13, 1752, 3110, 11, 438, 582, 614, 2669, 16588, 11, 30106, 3072, 315, 3015, 320, 39, 17, 46, 8, 374, 220, 16, 23, 575, 13, 5542, 1588, 582, 3535, 429, 220, 16, 23, 575, 3015, 702, 1172, 220, 16, 41930, 315, 3015, 11, 220, 16, 23, 342, 3015, 702, 220, 16, 34651, 34615, 315, 3015, 11, 429, 374, 11, 220, 21, 13, 15, 17, 17, 220, 16, 15, 17, 18, 34615, 315, 3015, 13, 18994, 1671, 1184, 279, 1372, 315, 32199, 323, 34615, 1393, 15331 ]	[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
India and the Contemporary World 112 The loss of the finest grazing lands and water resources created pressure on the small area of land that the Maasai were confined within. Continuous grazing within a small area inevitably meant a deterioration of the quality of pastures. Fodder was always in short supply. Feeding the cattle became a persistent problem. 3.2 The Borders are Closed In the nineteenth century, African pastoralists could move over vast areas in search of pastures. When the pastures were exhausted in one place they moved to a different area to graze their cattle. From the late nineteenth century, the colonial government began imposing various restrictions on their mobility. Like the Maasai, other pastoral groups were also forced to live within the confines of special reserves. The boundaries of these reserves became the limits within which they could now move. They were not allowed to move out with their stock without special permits. And it was difficult to get permits without trouble and harassment. Those found guilty of disobeying the rules were severely punished. Pastoralists were also not allowed to enter the markets in white areas. In many regions, they were prohibited from participating in any form of trade. White settlers and European colonists saw pastoralists as dangerous and savage people with whom all contact had to be minimised. Cutting off all links was, however, never really possible, because white colonists had to depend on black labour to bore mines and, build roads and towns. The new territorial boundaries and restrictions imposed on them suddenly changed the lives of pastoralists. This adversely affected Source F In most places in colonial Africa, the police were given instructions to keep a watch on the movements of pastoralists, and prevent them from entering white areas. The following is one such instruction given by a magistrate to the police, in south-west Africa, restricting the movements of the pastoralists of Kaokoland in Namibia Passes to enter the Territory should not be given to these Natives unless exceptional circumstances necessitate their entering The object of the above proclamation is to restrict the number of natives entering the Territory and to keep a check on them, and ordinary visiting passes should therefore never be issued to them. Kaokoveld permits to enter, Magistrate to Police Station Commanders of Outjo and Kamanjab, 24 November, 1937. 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SURFACE AREAS AND VOLUMES 251 Solution Radius of the hemispherical tank 3 2 m Volume of the tank 3 3 2 22 3 m 3 7 2 3 99 m 14 So, the volume of the water to be emptied 3 1 99 m 2 14 99 1000 28 litres 99000 28 litres Since, 25 7 litres of water is emptied in 1 second, 99000 28 litres of water will be emptied in 99000 7 28 25 seconds, i.e., in 16.5 minutes. EXERCISE 13.3 Take 22 7 , unless stated otherwise. 1. A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder. 2. Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere. 3. A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform. 4. A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment. 5. A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream. 6. 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SCIENCE 170 five and some animals, such as dogs can hear up to 25 kHz (1 kHz 1000 Hz). As people grow older their ears become less sensitive to higher frequencies. Sounds of frequencies below 20 Hz are called infrasonic sound or infrasound. If we could hear infrasound we would hear the vibrations of a pendulum just as we hear the vibrations of the wings of a bee. Rhinoceroses communicate using infrasound of frequency as low as 5 Hz. Whales and elephants produce sound in the infrasound range. It is observed that some animals get disturbed before earthquakes. Earthquakes produce low-frequency infrasound before the main shock waves begin which possibly alert the animals. Frequencies higher than 20 kHz are called ultrasonic sound or ultrasound. Ultrasound is produced by animals such as dolphins, bats and porpoises. Moths of certain families have very sensitive hearing equipment. These moths can hear the high frequency squeaks of the bat and know when a bat is flying nearby, and are able to escape capture. Rats also play games by producing ultrasound. Hearing Aid People with hearing loss may need a hearing aid. A hearing aid is an electronic, battery operated device. The hearing aid receives sound through a microphone. The microphone converts the sound waves to electrical signals. These electrical signals are amplified by an amplifier. The amplified electrical signals are given to a speaker of the hearing aid. The speaker converts the amplified electrical signal to sound and sends to the ear for clear hearing. uestions 1. What is the audible range of the average human ear? 2. What is the range of frequencies associated with (a) Infrasound? (b) Ultrasound? 12.5 Applications of Ultrasound Ultrasounds are high frequency waves. Ultrasounds are able to travel along well- defined paths even in the presence of obstacles. Ultrasounds are used extensively in industries and for medical purposes. Ultrasound is generally used to clean parts located in hard-to-reach places, for example, spiral tube, odd shaped parts, electronic components etc. Objects to be cleaned are placed in a cleaning solution and ultrasonic waves are sent into the solution. Due to the high frequency, the particles of dust, grease and dirt get detached and drop out. The objects thus get thoroughly cleaned. Ultrasounds can be used to detect cracks and flaws in metal blocks. Metallic components are generally used in construction of big structures like buildings, bridges, machines and also scientific equipment. The cracks or holes inside the metal blocks, which are invisible from outside reduces the strength of the structure. Ultrasonic waves are allowed to pass through the metal block and detectors are used to detect the transmitted waves. If there is even a small defect, the ultrasound gets reflected back indicating the presence of the flaw or defect, as shown in Fig. 12.16. 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16 Economics Overview The chapter People as Resource is an effort to explain population as an asset for the economy rather than a liability. Population becomes human capital when there is investment made in the form of education, training and medical care. In fact, human capital is the stock of skill and productive knowledge embodied in them. People as Resource is a way of referring to a countrys working people in terms of their existing productive skills and abilities. Looking at the population from this productive aspect emphasises its ability to contribute to the creation of the Gross National Product. Like other resources population also is a resource a human resource. This is the positive side of a large population that is often overlooked when we look only at the negative side, considering only the problems of providing the population with food, education and access to health facilities. When the existing human resource is further developed by becoming more educated and healthy, we call it human capital formation that adds to the productive power of the country just like physical capital formation. Investment in human capital (through education, training, medical care) yields a return just like investment in physical capital. This can be seen directly in the form of higher incomes earned because of higher productivity of the more educated or the better trained persons, as well as the higher productivity of healthier people. People as Resource 2 Chapter Indias Green Revolution is a dramatic example of how the input of greater knowledge in the form of improved production technologies can rapidly increase the productivity of scarce land resources. Indias IT revolution is a striking instance of how the importance of human capital has come to acquire a higher position than that of material, plant and machinery. Source Planning Commission, Govt. of India. 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Chemical Reactions and Equations Why does the iron nail become brownish in colour and the blue colour of copper sulphate solution fades? The following chemical reaction takes place in this Activity Fe(s) CuSO4(aq) FeSO4(aq) Cu(s) (1.24) (Copper sulphate) (Iron sulphate) In this reaction, iron has displaced or removed another element, copper, from copper sulphate solution. This reaction is known as displacement reaction. Other examples of displacement reactions are Zn(s) CuSO4(aq) ZnSO4(aq) Cu(s) (1.25) (Copper sulphate) (Zinc sulphate) Pb(s) CuCl2(aq) PbCl2(aq) Cu(s) (1.26) (Copper chloride) (Lead chloride) Zinc and lead are more reactive elements than copper. They displace copper from its compounds. Take about 3 mL of sodium sulphate solution in a test tube. In another test tube, take about 3 mL of barium chloride solution. Mix the two solutions (Fig. 1.9). What do you observe? Figure 1.9 Figure 1.9 Figure 1.9 Figure 1.9 Figure 1.9 Formation of barium sulphate and sodium chloride You will observe that a white substance, which is insoluble in water, is formed. This insoluble substance formed is known as a precipitate. Any reaction that produces a precipitate can be called a precipitation reaction. Na2SO4(aq) BaCl2(aq) BaSO4(s) 2NaCl(aq) (1.27) (Sodium (Barium (Barium (Sodium sulphate) chloride) sulphate) chloride) Figure 1.8 Figure 1.8 Figure 1.8 Figure 1.8 Figure 1.8 (b) Iron nails and copper sulphate solutions compared before and after the experiment 2019-20	[ 63838, 938, 1032, 4020, 323, 11702, 804, 8429, 1558, 279, 11001, 30995, 3635, 13876, 812, 304, 12463, 323, 279, 6303, 12463, 315, 23285, 82678, 349, 6291, 86409, 30, 576, 2701, 11483, 12720, 4990, 1992, 304, 419, 14981, 3841, 1141, 8, 26462, 13880, 19, 2877, 80, 8, 3841, 13880, 19, 2877, 80, 8, 26462, 1141, 8, 320, 16, 13, 17, 19, 8, 320, 34, 18487, 82678, 349, 8, 320, 46393, 82678, 349, 8, 758, 419, 12720, 11, 11001, 702, 48146, 476, 6963, 2441, 2392, 11, 23285, 11, 504, 23285, 82678, 349, 6291, 13, 1096, 12720, 374, 3881, 438, 43053, 12720, 13, 6944, 10295, 315, 43053, 24473, 525, 1863, 77, 1141, 8, 26462, 13880, 19, 2877, 80, 8, 1863, 77, 13880, 19, 2877, 80, 8, 26462, 1141, 8, 320, 16, 13, 17, 20, 8, 320, 34, 18487, 82678, 349, 8, 320, 57, 2840, 82678, 349, 8, 97354, 1141, 8, 26462, 5066, 17, 2877, 80, 8, 97354, 5066, 17, 2877, 80, 8, 26462, 1141, 8, 320, 16, 13, 17, 21, 8, 320, 34, 18487, 81782, 8, 320, 53863, 81782, 8, 95399, 323, 2990, 525, 803, 55463, 5424, 1091, 23285, 13, 2379, 827, 2007, 23285, 504, 1181, 31146, 13, 11778, 911, 220, 18, 64070, 315, 38595, 82678, 349, 6291, 304, 264, 1273, 13705, 13, 758, 2441, 1273, 13705, 11, 1896, 911, 220, 18, 64070, 315, 3619, 2356, 81782, 6291, 13, 19219, 279, 1378, 9904, 320, 28935, 13, 220, 16, 13, 24, 568, 3555, 653, 498, 22986, 30, 19037, 220, 16, 13, 24, 19037, 220, 16, 13, 24, 19037, 220, 16, 13, 24, 19037, 220, 16, 13, 24, 19037, 220, 16, 13, 24, 71366, 315, 3619, 2356, 82678, 349, 323, 38595, 81782, 1446, 686, 22986, 429, 264, 4158, 19699, 11, 892, 374, 84843, 40472, 304, 3015, 11, 374, 14122, 13, 1096, 84843, 40472, 19699, 14122, 374, 3881, 438, 264, 35741, 19652, 13, 5765, 12720, 429, 18644, 264, 35741, 19652, 646, 387, 2598, 264, 59950, 12720, 13, 12812, 17, 13880, 19, 2877, 80, 8, 14322, 5066, 17, 2877, 80, 8, 14322, 13880, 19, 1141, 8, 220, 17, 16193, 5066, 2877, 80, 8, 320, 16, 13, 17, 22, 8, 320, 50, 46776, 320, 3428, 2356, 320, 3428, 2356, 320, 50, 46776, 82678, 349, 8, 81782, 8, 82678, 349, 8, 81782, 8, 19037, 220, 16, 13, 23, 19037, 220, 16, 13, 23, 19037, 220, 16, 13, 23, 19037, 220, 16, 13, 23, 19037, 220, 16, 13, 23, 320, 65, 8, 16570, 39843, 323, 23285, 82678, 349, 9904, 7707, 1573, 323, 1283, 279, 9342, 220, 17, 15, 16, 24, 12, 17, 15, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645, 151645 ]	[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
STATISTICS 285 Solution Class intervals Frequency Cumulative frequency 0 - 100 2 2 100 - 200 5 7 200 - 300 x 7 x 300 - 400 12 19 x 400 - 500 17 36 x 500 - 600 20 56 x 600 - 700 y 56 x y 700 - 800 9 65 x y 800 - 900 7 72 x y 900 - 1000 4 76 x y It is given that n 100 So, 76 x y 100, i.e., x y 24 (1) The median is 525, which lies in the class 500 600 So, l 500, f 20, cf 36 x, h 100 Using the formula Median cf 2 , n l h f we get 525 50 36 500 100 20 x i.e., 525 500 (14 x) 5 i.e., 25 70 5x i.e., 5x 70 25 45 So, x 9 Therefore, from (1), we get 9 y 24 i.e., y 15 2019-20	[ 22595, 71637, 220, 17, 23, 20, 12478, 3228, 26992, 42380, 31578, 22160, 11639, 220, 15, 481, 220, 16, 15, 15, 220, 17, 220, 17, 220, 16, 15, 15, 481, 220, 17, 15, 15, 220, 20, 220, 22, 220, 17, 15, 15, 481, 220, 18, 15, 15, 856, 220, 22, 856, 220, 18, 15, 15, 481, 220, 19, 15, 15, 220, 16, 17, 220, 16, 24, 856, 220, 19, 15, 15, 481, 220, 20, 15, 15, 220, 16, 22, 220, 18, 21, 856, 220, 20, 15, 15, 481, 220, 21, 15, 15, 220, 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NATURAL RESOURCES 199 adds to the carbon dioxide in the atmosphere is the process of combustion where fuels are burnt to provide energy for various needs like heating, cooking, transportation and industrial processes. In fact, the percentage of carbon dioxide in the atmosphere is said to have doubled since the industrial revolution when human beings started burning fossil fuels on a very large scale. Carbon, like water, is thus cycled repeatedly through different forms by the various physical and biological activities. 14.4.3 (i) THE GREENHOUSE EFFECT Recall the reading taken by you under (iii) in Activity 14.1. Heat is trapped by glass, and hence the temperature inside a glass enclosure will be much higher than the surroundings. This phenomenon was used to create an enclosure where tropical plants Fig. 14.7 Carbon-cycle in nature could be kept warm during the winters in colder climates. Such enclosures are called greenhouses. Greenhouses have also lent their name to an atmospheric phenomenon. Some gases prevent the escape of heat from the Earth. An increase in the percentage of such gases in the atmosphere would cause the average temperatures to increase world-wide and this is called the greenhouse effect. Carbon dioxide is one of the greenhouse gases. An increase in the carbon dioxide content in the atmosphere would cause more heat to be retained by the atmosphere and lead to global warming. Activity 14.12 Find out what the consequences of global warming would be. 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20 Democratic Politics When the demand for the formation of States on the basis of language was raised, some national leaders feared that it would lead to the disintegration of the country. The Central Government resisted linguistic States for some time. But the experience has shown that the formation of linguistic States has actually made the country, more united. It has also made administration easier. Language policy A second test for Indian federation is the language policy. Our Constitution did not give the status of national language to any one language. Hindi was identified as the official language. But Hindi is the mother tongue of only about 40 per cent of Indians. Therefore, there were many safeguards to protect other languages. Besides Hindi, there are 21 other languages recognised as Scheduled Languages by the Constitution. A candidate in an examination conducted for the Central Government positions may opt to take the examination in any of these languages. States too have their own official languages. Much of the government work takes place in the official language of the concerned State. Unlike Sri Lanka, the leaders of our country adopted a very cautious attitude in spreading the use of Hindi. According to the Constitution, the use of English for official purposes was to stop in 1965. However, many non- Hindi speaking States demanded that the use of English continue. In Tamil Nadu, this movement took a violent form. The Central Government responded by agreeing to continue the use of English along with Hindi for official purposes. Many critics think that this solution favoured the English- speaking elite. Promotion of Hindi continues to be the official policy of the Government of India. Promotion does not mean that the Central Government can impose Hindi on States where people speak a different language. The flexibility shown by Indian political leaders helped our country avoid the kind of situation that Sri Lanka finds itself in. Centre-State relations Restructuring the Centre-State relations is one more way in which federalism has been strengthened in practice. How the constitutional arrangements for sharing power work in reality depends to a large extent on how the ruling parties and leaders follow these arrangements. For a long time, the same party ruled both at the Centre and in most of the States. This meant that the State governments did not exercise their rights as autonomous federal units. As and when the ruling party at the State level was different, the parties that ruled at the Centre tried to undermine the power of the States. In those days, the Central Government would often misuse the Constitution to dismiss the State governments that were controlled by rival parties. This undermined the spirit of federalism. All this changed significantly after 1990. This period saw the rise of regional political parties in many States of the country. This was also the beginning of the era of COALITION GOVERNMENTS at the Centre. Since no single party got a clear majority in the Lok Sabha, the major national parties had to enter into an alliance with many parties including several regional parties to form a government at the Centre. This led to a new culture of power sharing and respect for the autonomy of State Governments. This trend was Coalition government A government formed by the coming together of at least two political parties. Usually partners in a coalition form a political alliance and adopt a common programme. Why Hindi? Why not Bangla or Telugu? 2018-19

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Science W e see a variety of objects in the world around us. However, we are unable to see anything in a dark room. On lighting up the room, things become visible. What makes things visible? During the day, the sunlight helps us to see objects. An object reflects light that falls on it. This reflected light, when received by our eyes, enables us to see things. We are able to see through a transparent medium as light is transmitted through it. There are a number of common wonderful phenomena associated with light such as image formation by mirrors, the twinkling of stars, the beautiful colours of a rainbow, bending of light by a medium and so on. A study of the properties of light helps us to explore them. By observing the common optical phenomena around us, we may conclude that light seems to travel in straight lines. The fact that a small source of light casts a sharp shadow of an opaque object points to this straight-line path of light, usually indicated as a ray of light. If an opaque object on the path of light becomes very small, light has a tendency to bend around it and not walk in a straight line an effect known as the diffraction of light. Then the straight-line treatment of optics using rays fails. To explain phenomena such as diffraction, light is thought of as a wave, the details of which you will study in higher classes. Again, at the beginning of the 20th century, it became known that the wave theory of light often becomes inadequate for treatment of the interaction of light with matter, and light often behaves somewhat like a stream of particles. This confusion about the true nature of light continued for some years till a modern quantum theory of light emerged in which light is neither a wave nor a particle the new theory reconciles the particle properties of light with the wave nature. In this Chapter, we shall study the phenomena of reflection and refraction of light using the straight-line propagation of light. These basic concepts will help us in the study of some of the optical phenomena in nature. We shall try to understand in this Chapter the reflection of light by spherical mirrors and refraction of light and their application in real life situations. A highly polished surface, such as a mirror, reflects most of the light falling on it. You are already familiar with the laws of reflection of light. 2019-20

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250 MATHEMATICS Solution The volume of water in the overhead tank equals the volume of the water removed from the sump. Now, the volume of water in the overhead tank (cylinder) r2h 3.14 0.6 0.6 0.95 m3 The volume of water in the sump when full l b h 1.57 1.44 0.95 m3 The volume of water left in the sump after filling the tank (1.57 1.44 0.95) (3.14 0.6 0.6 0.95) m3 (1.57 0.6 0.6 0.95 2) m3 So, the height of the water left in the sump volume of water left in the sump l b 1.57 0.6 0.6 0.95 2 m 1.57 1.44 0.475 m 47.5 cm Also, Capacity of tank Capacity of sump 3.14 0.6 0.6 0.95 1 1.57 1.44 0.95 2 Therefore, the capacity of the tank is half the capacity of the sump. Example 10 A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire. Solution The volume of the rod 2 3 3 1 8 cm 2 cm 2 . The length of the new wire of the same volume 18 m 1800 cm If r is the radius (in cm) of cross-section of the wire, its volume r2 1800 cm3 Therefore, r2 1800 2 i.e., r2 1 900 i.e., r 1 30 So, the diameter of the cross section, i.e., the thickness of the wire is 1 15 cm, i.e., 0.67mm (approx.). Example 11 A hemispherical tank full of water is emptied by a pipe at the rate of 4 37 litres per second. How much time will it take to empty half the tank, if it is 3m in diameter? (Take 22 7 ) 2019-20

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92 MATHEMATICS 6.3 Intersecting Lines and Non-intersecting Lines Draw two different lines PQ and RS on a paper. You will see that you can draw them in two different ways as shown in Fig. 6.5 (i) and Fig. 6.5 (ii). (i) Intersecting lines (ii) Non-intersecting (parallel) lines Fig. 6.5 Different ways of drawing two lines Recall the notion of a line, that it extends indefinitely in both directions. Lines PQ and RS in Fig. 6.5 (i) are intersecting lines and in Fig. 6.5 (ii) are parallel lines. Note that the lengths of the common perpendiculars at different points on these parallel lines is the same. This equal length is called the distance between two parallel lines. 6.4 Pairs of Angles In Section 6.2, you have learnt the definitions of some of the pairs of angles such as complementary angles, supplementary angles, adjacent angles, linear pair of angles, etc. Can you think of some relations between these angles? Now, let us find out the relation between the angles formed when a ray stands on a line. Draw a figure in which a ray stands on a line as shown in Fig. 6.6. Name the line as AB and the ray as OC. What are the angles formed at the point O? They are AOC, BOC and AOB. Can we write AOC BOC AOB? (1) Yes! (Why? Refer to adjacent angles in Section 6.2) What is the measure of AOB? It is 180. (Why?) (2) From (1) and (2), can you say that AOC BOC 180? Yes! (Why?) From the above discussion, we can state the following Axiom Fig. 6.6 Linear pair of angles 2019-2020

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Po w e r-sh a r i n g 1 Chapter I Power-sharing Overview With this chapter, we resume the tour of democracy that we started last year. We noted last year that in a democracy all power does not rest with any one organ of the government. An intelligent sharing of power among legislature, executive and judiciary is very important to the design of a democracy. In this and the next two chapters, we carry this idea of power-sharing forward. We start with two stories from Belgium and Sri Lanka. Both these stories are about how democracies handle demands for power-sharing.The stories yield some general conclusions about the need for power-sharing in democracy. This allows us to discuss various forms of power-sharing that will be taken up in the following two chapters. 2018-19

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52 CONTEMPORARY INDIA-I 2. Answer the following questions briefly. (i) What factors are responsible for the distribution of plants and animals in India? (ii) What is a bio-reserve? Give two examples. (iii) Name two animals having habitat in tropical and montane type of vegetation. 3. Distinguish between (i) Flora and Fauna (ii) Tropical Evergreen and Deciduous forests 4. Name different types of Vegetation found in India and describe the vegetation of high altitudes. 5. Quite a few species of plants and animals are endangered in India. Why? 6. Why has India a rich heritage of flora and fauna? Map Skills On an outline map of India, label the following. (i) Areas of Evergreen Forests (ii) Areas of Dry Deciduous Forests (iii) Two national parks each in Northern, Southern, Eastern and Western parts of the Country ProjectActivity (i) Find some trees in your neighbourhood having medicinal values. (ii) Find ten occupations getting raw material from forests and wildlife. (iii) Write a poem or paragraph showing the importance of wildlife. (iv) Write the script of a street play giving the importance of tree plantation and try to enact it in your locality. (v) Plant a tree either on your birthday or one of your family members birthday. Note the growth of the tree and notice in which season it grows faster. 2019-20

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196 India and the Contemporary World education, and returns as the judge in the local court. Meanwhile, the villagers, thinking that the landlords men had killed him, file a case. At the conclusion of the trial, the judge reveals his true identity, and the Nambuthiri repents and reforms his ways. Saraswativijayam stresses the importance of education for the upliftment of the lower castes. From the 1920s, in Bengal too a new kind of novel emerged that depicted the lives of peasants and low castes. Advaita Malla Burmans (1914-51) Titash Ekti Nadir Naam (1956) is an epic about the Mallas, a community of fisherfolk who live off fishing in the river Titash. The novel is about three generations of the Mallas, about their recurring tragedies and the story of Ananta, a child born of parents who were tragically separated after their wedding night. Ananta leaves the community to get educated in the city. The novel describes the community life of the Mallas in great detail, their Holi and Kali Puja festivals, boat races, bhatiali songs, their relationships of friendship and animosity with the peasants and the oppression of the upper castes. Slowly the community breaks up and the Mallas start fighting amongst themselves as new cultural influences from the city start penetrating their lives. The life of the community and that of the river is intimately tied. Their end comes together as the river dries up, the community dies too. While novelists before Burman had featured low castes as their protagonists, Titash is special because the author is himself from a low-caste, fisherfolk community. Over time, the medium of the novel made room for the experiences of communities that had not received much space in the literary scene earlier. Vaikkom Muhammad Basheer (1908-94), for example, was one of the early Muslim writers to gain wide renown as a novelist in Malayalam. Basheer had little formal education. Most of his works were based on his own rich personal experience rather than on books from the past. When he was in class five at school, Basheer left home to take part in the Salt Satyagraha. Later he spent years wandering in different parts of India and travelling even to Arabia, working in a ship, living with Sufis and Hindu sanyasis, and training as a wrestler. Basheers short novels and stories were written in the ordinary language of conversation. With wonderful humour, Basheers novels spoke about details from the everyday life of Muslim households. He also brought into Malayalam writing themes which were considered very unusual at that time poverty, insanity and life in prisons. Fig. 23 Basheer carrying books. In his early years as a writer, Basheer had great difficulty earning a living from his books. He often sold them himself, carrying copies personally to houses and shops. In some of his stories, Basheer wrote about his days as a vendor of his own books. 2018-19

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STATISTICS 269 Example 3 The distribution below shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean number of wickets by choosing a suitable method. What does the mean signify? Number of 20 - 60 60 - 100 100 - 150 150 - 250 250 - 350 350 - 450 wickets Number of 7 5 16 12 2 3 bowlers Solution Here, the class size varies, and the xi ,s are large. Let us still apply the step- deviation method with a 200 and h 20. Then, we obtain the data as in Table 14.8. Table 14.8 Number of Number of xi di xi 200 20 i i d u ui fi wickets bowlers taken ( fi) 20 - 60 7 40 160 8 56 60 - 100 5 80 120 6 30 100 - 150 16 125 75 3.75 60 150 - 250 12 200 0 0 0 250 - 350 2 300 100 5 10 350 - 450 3 400 200 10 30 Total 45 106 So, 106 45 u Therefore, x 200 106 20 45 200 47.11 152.89. This tells us that, on an average, the number of wickets taken by these 45 bowlers in one-day cricket is 152.89. Now, let us see how well you can apply the concepts discussed in this section! 2019-20

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106 MATHEMATICS Theorem 6.8 If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles. It is obvious from the above theorem that an exterior angle of a triangle is greater than either of its interior apposite angles. Now, let us take some examples based on the above theorems. Example 7 In Fig. 6.37, if QT PR, TQR 40 and SPR 30, find x and y. Solution In TQR, 90 40 x 180 (Angle sum property of a triangle) Therefore, x 50 Now, y SPR x (Theorem 6.8) Therefore, y 30 50 80 Example 8 In Fig. 6.38, the sides AB and AC of ABC are produced to points E and D respectively. If bisectors BO and CO of CBE and BCD respectively meet at point O, then prove that BOC 90 1 2 BAC. Solution Ray BO is the bisector of CBE. Therefore, CBO 1 2 CBE 1 2 (180 y) 90 2 y (1) Similarly, ray CO is the bisector of BCD. Therefore, BCO 1 2 BCD 1 2 (180 z) 90 2 z (2) Fig. 6.37 Fig. 6.38 2019-2020

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8 MATHEMATICS In the same way, you can locate n for any positive integer n, after 1 n has been located. EXERCISE 1.2 1. State whether the following statements are true or false. Justify your answers. (i) Every irrational number is a real number. (ii) Every point on the number line is of the form m , where m is a natural number. (iii) Every real number is an irrational number. 2. Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number. 3. Show how 5 can be represented on the number line. 4. Classroom activity (Constructing the square root spiral) Take a large sheet of paper and construct the square root spiral in the following fashion. Start with a point O and draw a line segment OP1 of unit length. Draw a line segment P1P2 perpendicular to OP1 of unit length (see Fig. 1.9). Now draw a line segment P2P3 perpendicular to OP2. Then draw a line segment P3P4 perpendicular to OP3. Continuing in this manner, you can get the line segment Pn1Pn by drawing a line segment of unit length perpendicular to OPn1. In this manner, you will have created the points P2, P3,...., Pn,... ., and joined them to create a beautiful spiral depicting 2, 3, 4, ... 1.3 Real Numbers and their Decimal Expansions In this section, we are going to study rational and irrational numbers from a different point of view. We will look at the decimal expansions of real numbers and see if we can use the expansions to distinguish between rationals and irrationals. We will also explain how to visualise the representation of real numbers on the number line using their decimal expansions. Since rationals are more familiar to us, let us start with them. Let us take three examples 10 7 1 , , 3 8 7 . Pay special attention to the remainders and see if you can find any pattern. Fig. 1.9 Constructing square root spiral 2019-2020

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195 Novels, Society and History It is not surprising that many men were suspicious of women writing novels or reading them. This suspicion cut across communities. Hannah Mullens, a Christian missionary and the author of Karuna o Phulmonir Bibaran (1852), reputedly the first novel in Bengali, tells her readers that she wrote in secret. In the twentieth century, Sailabala Ghosh Jaya, a popular novelist, could only write because her husband protected her. As we have seen in the case of the south, women and girls were often discouraged from reading novels. 4.1 Caste Practices, Lower-Castes and Minorities As you have seen, Indulekha was a love story. But it was also about an issue that was hotly debated at the time when the novel was written. This concerned the marriage practices of upper-caste Hindus in Kerala, especially the Nambuthiri Brahmins and the Nayars. Nambuthiris were also major landlords in Kerala at that time and a large section of the Nayars were their tenants. In late-nineteenth- century Kerala, a younger generation of English-educated Nayar men who had acquired property and wealth on their own, began arguing strongly against Nambuthiri alliances with Nayar women. They wanted new laws regarding marriage and property. The story of Indulekha is interesting in the light of these debates. Suri Nambuthiri, the foolish landlord who comes to marry Indulekha, is the focus of much satire in the novel. The intelligent heroine rejects him and chooses Madhavan, the educated and handsome Nayar as her husband, and the young couple move to Madras, where Madhavan joins the civil service. Suri Nambuthiri, desperate to find a partner for himself, finally marries a poorer relation from the same family and goes away pretending that he has married Indulekha! Chandu Menon clearly wanted his readers to appreciate the new values of his hero and heroine and criticise the ignorance and immorality of Suri Nambuthiri. Novels like Indirabai and Indulekha were written by members of the upper castes, and were primarily about upper-caste characters. But not all novels were of this kind. Potheri Kunjambu, a lower-caste writer from north Kerala, wrote a novel called Saraswativijayam in 1892, mounting a strong attack on caste oppression. This novel shows a young man from an untouchable caste, leaving his village to escape the cruelty of his Brahmin landlord. He converts to Christianity, obtains modern Women with books These days we can see women in black bordered sarees with massive books in their hands, walking inside their houses. Often seeing them with these books in hand, their brothers or husbands are seized with fear in case they are asked for meanings. Sadharani, 1880. Box 8 Fig. 22 Malabar Beauty, painting by Ravi Varma. Chandu Menon thought that the novel was similar to new trends in Indian painting. One of the foremost oil painters of this time was Raja Ravi Varma (1848- 1906). Chandu Menons description of his heroines may have been guided by some of his paintings. 2018-19

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Acids, Bases and Salts What is the pH of the soil in your backyard? Plants require a specific pH range for their healthy growth. To find out the pH required for the healthy growth of a plant, you can collect the soil from various places and check the pH in the manner described below in Activity 2.12. Also, you can note down which plants are growing in the region from which you have collected the soil. Acids in other planets The atmosphere of venus is made up of thick white and yellowish clouds of sulphuric acid. Do you think life can exist on this planet? Put about 2 g soil in a test tube and add 5 mL water to it. Shake the contents of the test tube. Filter the contents and collect the filtrate in a test tube. Check the pH of this filtrate with the help of universal indicator paper. What can you conclude about the ideal soil pH for the growth of plants in your region? pH in our digestive system It is very interesting to note that our stomach produces hydrochloric acid. It helps in the digestion of food without harming the stomach. During indigestion the stomach produces too much acid and this causes pain and irritation. To get rid of this pain, people use bases called antacids. One such remedy must have been suggested by you at the beginning of this Chapter. These antacids neutralise the excess acid. Magnesium hydroxide (Milk of magnesia), a mild base, is often used for this purpose. pH change as the cause of tooth decay Tooth decay starts when the pH of the mouth is lower than 5.5. Tooth enamel, made up of calcium hydroxyapatite (a crystalline form of calcium phosphate) is the hardest substance in the body. It does not dissolve in water, but is corroded when the pH in the mouth is below 5.5. Bacteria present in the mouth produce acids by degradation of sugar and food particles remaining in the mouth after eating. The best way to prevent this is to clean the mouth after eating food. Using toothpastes, which are generally basic, for cleaning the teeth can neutralise the excess acid and prevent tooth decay. Self defence by animals and plants through chemical warfare Have you ever been stung by a honey-bee? Bee-sting leaves an acid which causes pain and irritation. Use of a mild base like baking soda on the stung area gives relief. Stinging hair of nettle leaves inject methanoic acid causing burning pain. 2019-20

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TRIANGLES 139 Fig. 6.34 2. In Fig. 6.35, ODC OBA, BOC 125 and CDO 70. Find DOC, DCO and OAB. 3. Diagonals AC and BD of a trapezium ABCD with AB DC intersect each other at the point O. Using a similarity criterion for two triangles, show that OA OB OC OD Fig. 6.35 2019-20

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316 MATHEMATICS Now, we also have to find the number of years by which the enrolment will reach 50. So, we have to find the value of n in the equation or formula 50 41.9 0.22n (2) Step 2 Solution Solving (2) for n, we get n 50 41.9 8.1 36.8 0.22 0.22 Step 3 Interpretation Since the number of years is an integral value, we will take the next higher integer, 37. So, the enrolment percentage will reach 50 in 1991 37 2028. In a word problem, we generally stop here. But, since we are dealing with a real- life situation, we have to see to what extent this value matches the real situation. Step 4 Validation Let us check if Formula (2) is in agreement with the reality. Let us find the values for the years we already know, using Formula (2), and compare it with the known values by finding the difference. The values are given in Table A2.4. Table A2.4 Year Enrolment Values given by (2) Difference (in ) (in ) (in ) 0 41.9 41.90 0 1 42.6 42.12 0.48 2 42.7 42.34 0.36 3 42.9 42.56 0.34 4 43.1 42.78 0.32 5 43.2 43.00 0.20 6 43.5 43.22 0.28 7 43.5 43.44 0.06 8 43.6 43.66 0.06 9 43.7 43.88 0.18 10 44.1 44.10 0.00 As you can see, some of the values given by Formula (2) are less than the actual values by about 0.3 or even by 0.5. This can give rise to a difference of about 3 to 5 years since the increase per year is actually 1 to 2. We may decide that this 2019-2020

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25 Nationalism in Europe Fig. 19 Germania guarding the Rhine. In 1860, the artist Lorenz Clasen was commissioned to paint this image. The inscription on Germanias sword reads The German sword protects the German Rhine. Look once more at Fig. 10. Imagine you were a citizen of Frankfurt in March 1848 and were present during the proceedings of the parliament. How would you (a) as a man seated in the hall of deputies, and (b) as a woman observing from the galleries, relate to the banner of Germania hanging from the ceiling? Activity 2018-19

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Forest Society and Colonialism 75 In Section II we will shift our focus to the study of livelihoods and economies. We will look at how the lives of forest dwellers and pastoralists changed in the modern world and how they played a part in shaping these changes. All too often in looking at the emergence of the modern world, we only focus on factories and cities, on the industrial and agricultural sectors which supply the market. But we forget that there are other economies outside these sectors, other people too who matter to the nation. To modern eyes, the lives of pastoralists and forest dwellers, the shifting cultivators and food gatherers often seem to be stuck in the past. It is as if their lives are not important when we study the emergence of the contemporary world. The chapters in Section II will suggest that we need to know about their lives, see how they organise their world and operate their economies. These communities are very much part of the modern world we live in today. They are not simply survivors from a bygone era. Chapter IV will take you into the forest and tell you about the variety of ways the forests were used by communities living within them. It will show how in the nineteenth century the growth of industries and urban centres, ships and railways, created a new demand on the forests for timber and other forest products. New demands led to new rules of forest use, new ways of organising the forest. You will see how colonial control was established over the forests, how forest areas were mapped, trees were classified, and plantations were developed. All these developments affected the lives of those local communities who used forest resources. They were forced to operate within new systems and reorganise their lives. But they also rebelled against the rules and persuaded the state to change its policies. The chapter will give you an idea of the history of such developments in India and Indonesia. SECTION II LIVELIHOODS, ECONOMIES AND SOCIETIES LIVELIHOODS, ECONOMIES AND SOCIETIES 2019-2020

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Pastoralists in the Modern World 101 Activity Source B In Karnataka and Andhra Pradesh, again, the dry central plateau was covered with stone and grass, inhabited by cattle, goat and sheep herders. The Gollas herded cattle. The Kurumas and Kurubas reared sheep and goats and sold woven blankets. They lived near the woods, cultivated small patches of land, engaged in a variety of petty trades and took care of their herds. Unlike the mountain pastoralists, it was not the cold and the snow that defined the seasonal rhythms of their movement rather it was the alternation of the monsoon and dry season. In the dry season they moved to the coastal tracts, and left when the rains came. Only buffaloes liked the swampy, wet conditions of the coastal areas during the monsoon months. Other herds had to be shifted to the dry plateau at this time. Banjaras were yet another well-known group of graziers. They were to be found in the villages of Uttar Pradesh, Punjab, Rajasthan, Madhya Pradesh and Maharashtra. In search of good pastureland for their cattle, they moved over long distances, selling plough cattle and other goods to villagers in exchange for grain and fodder. The accounts of many travellers tell us about the life of pastoral groups. In the early nineteenth century, Buchanan visited the Gollas during his travel through Mysore. He wrote Their families live in small villages near the skirt of the woods, where they cultivate a little ground, and keep some of their cattle, selling in the towns the produce of the dairy. Their families are very numerous, seven to eight young men in each being common. Two or three of these attend the flocks in the woods, while the remainder cultivate their fields, and supply the towns with firewood, and with straw for thatch. From Francis Hamilton Buchanan, A Journey from Madras through the Countries of Mysore, Canara and Malabar (London, 1807). Read Sources A and B. Write briefly about what they tell you about the nature of the work undertaken by men and women in pastoral households. Why do you think pastoral groups often live on the edges of forests? In the deserts of Rajasthan lived the Raikas. The rainfall in the region was meagre and uncertain. On cultivated land, harvests fluctuated every year. Over vast stretches no crop could be grown. So the Raikas combined cultivation with pastoralism. During the monsoons, the Raikas of Barmer, Jaisalmer, Jodhpur and Bikaner stayed in their home villages, where pasture was available. By October, when these grazing grounds were dry and exhausted, they moved out in search of other pasture and water, and returned again during the next monsoon. One group of Raikas known as the Maru (desert) Raikas herded camels and another group reared sheep and goat. Fig.6 A camel herder in his settlement. This is on the Thar desert near Jaisalmer in Rajasthan. The camel herders of the region are Maru (desert) Raikas, and their settlement is called a dhandi. 2019-2020

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The organised sector offers jobs that are the most sought-after. But the employment opportunities in the organised sector have been expanding very slowly. It is also common to find many organised sector enterprises in the unorganised sector. They adopt such strategies to evade taxes and refuse to follow laws that protect labourers. As a result, a large number of workers are forced to enter the unorganised sector jobs, which pay a very low salary. They are often exploited and not paid a fair wage. Their earnings are low and not regular. These jobs are not secure and have no other benefits. Since the 1990s, it is also common to see a large number of workers losing their jobs in the organised sector. These workers are forced to take up jobs in the unorganised sector with low earnings. Hence, besides the need for more work, there is also a need for protection and support of the workers in the unorganised sector. Who are these vulnerable people who need protection? In the rural areas, the unorganised sector mostly comprises of landless agricultural labourers, small and marginal farmers, sharecroppers and artisans (such as weavers, blacksmiths, carpenters and goldsmiths). Nearly 80 per cent of rural households in India are in small and marginal farmer category. These farmers need to be supported through adequate facility for timely delivery of seeds, agricultural inputs, credit, storage facilities and marketing outlets. In the urban areas, unorganised sector comprises mainly of workers in small-scale industry, casual workers in construction, trade and transport etc., and those who work as street vendors, head load workers, garment makers, rag pickers etc. Small-scale industry also needs governments support for procuring raw material and marketing of output. The casual workers in both rural and urban areas need to be protected. We also find that majority of workers from scheduled castes, tribes and backward communities find themselves in the unorganised sector. Besides getting the irregular and low paid work, these workers also face social discrimination. Protection and support to the unorganised sector workers is thus necessary for both economic and social development. When factories close down, many once regular workers are found selling goods or pushing a cart or doing some other odd job 2019-20

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168 MATHEMATICS CHAPTER 10 CIRCLES 10.1 Introduction You may have come across many objects in daily life, which are round in shape, such as wheels of a vehicle, bangles, dials of many clocks, coins of denominations 50 p, Re 1 and Rs 5, key rings, buttons of shirts, etc. (see Fig.10.1). In a clock, you might have observed that the seconds hand goes round the dial of the clock rapidly and its tip moves in a round path. This path traced by the tip of the seconds hand is called a circle. In this chapter, you will study about circles, other related terms and some properties of a circle. Fig. 10.1 2019-2020

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Life Processes design in multi-cellular organisms are followed, a specialised tissue for excretion will be developed, which means that the transportation system will need to transport waste away from cells to this excretory tissue. Let us consider these various processes, so essential to maintain life, one by one. 1. Why is diffusion insufficient to meet the oxygen requirements of multi- cellular organisms like humans? 2. What criteria do we use to decide whether something is alive? 3. What are outside raw materials used for by an organism? 4. What processes would you consider essential for maintaining life? When we walk or ride a bicycle, we are using up energy. Even when we are not doing any apparent activity, energy is needed to maintain a state of order in our body. We also need materials from outside in order to grow, develop, synthesise protein and other substances needed in the body. This source of energy and materials is the food we eat. How do living things get their food? The general requirement for energy and materials is common in all organisms, but it is fulfilled in different ways. Some organisms use simple food material obtained from inorganic sources in the form of carbon dioxide and water. These organisms, the autotrophs, include green plants and some bacteria. Other organisms utilise complex substances. These complex substances have to be broken down into simpler ones before they can be used for the upkeep and growth of the body. To achieve this, organisms use bio-catalysts called enzymes. Thus, the heterotrophs survival depends directly or indirectly on autotrophs. Heterotrophic organisms include animals and fungi. Carbon and energy requirements of the autotrophic organism are fulfilled by photosynthesis. It is the process by which autotrophs take in substances from the outside and convert them into stored forms of energy. This material is taken in the form of carbon dioxide and water which is converted into carbohydrates in the presence of sunlight and chlorophyll. Carbohydrates are utilised for providing energy to the plant. We will study how this takes place in the next section. The carbohydrates which are not used immediately are stored in the form of starch, which serves as the internal energy reserve to be used as and when required by the plant. A somewhat similar situation is seen in us where some of the energy derived from the food we eat is stored in our body in the form of glycogen. 2019-20

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Carbon and its Compounds Ethanoic acid is commonly called acetic acid and belongs to a group of acids called carboxylic acids. 5-8 solution of acetic acid in water is called vinegar and is used widely as a preservative in pickles. The melting point of pure ethanoic acid is 290 K and hence it often freezes during winter in cold climates. This gave rise to its name glacial acetic acid. The group of organic compounds called carboxylic acids are obviously characterised by their acidic nature. However, unlike mineral acids like HCl, which are completely ionised, carboxylic acids are weak acids. Compare the pH of dilute acetic acid and dilute hydrochloric acid using both litmus paper and universal indicator. Are both acids indicated by the litmus test? Does the universal indicator show them as equally strong acids? Take 1 mL ethanol (absolute alcohol) and 1 mL glacial acetic acid along with a few drops of concentrated sulphuric acid in a test tube. Warm in a water-bath for at least five minutes as shown in Fig. 4.11. Pour into a beaker containing 20-50 mL of water and smell the resulting mixture. Reactions of ethanoic acid (i) Esterification reaction Esters are most commonly formed by reaction of an acid and an alcohol. Ethanoic acid reacts with absolute ethanol in the presence of an acid catalyst to give an ester CH COOH CH CH OH CH C C CH CH H O 3 3 2 3 2 3 2 Acid O (E 11 thanoic acid) (Ethanol) (Ester) Generally, esters are sweet-smelling substances. These are used in making perfumes and as flavouring agents. On treating with sodium hydroxide, which is an alkali, the ester is converted back to alcohol and sodium salt of carboxylic acid. This reaction is known as saponification because it is used in the preparation of soap. Soaps are sodium or potassium salts of long chain carboxylic acid. Figure 4.11 Figure 4.11 Figure 4.11 Figure 4.11 Figure 4.11 Formation of ester Alcohol as a fuel Sugarcane plants are one of the most efficient convertors of sunlight into chemical energy. Sugarcane juice can be used to prepare molasses which is fermented to give alcohol (ethanol). Some countries now use alcohol as an additive in petrol since it is a cleaner fuel which gives rise to only carbon dioxide and water on burning in sufficient air (oxygen). 2019-20

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PROOFS IN MATHEMATICS 293 2. Once again you are given four cards. Each card has a number printed on one side and a letter on the other side. Which are the only two cards you need to turn over to check whether the following rule holds? If a card has a consonant on one side, then it has an odd number on the other side. A1.4 Theorems, Conjectures and Axioms So far we have discussed statements and how to check their validity. In this section, you will study how to distinguish between the three different kinds of statements mathematics is built up from, namely, a theorem, a conjecture and an axiom. You have already come across many theorems before. So, what is a theorem? A mathematical statement whose truth has been established (proved) is called a theorem. For example, the following statements are theorems, as you will see in Section A1.5. Theorem A1.1 The sum of the interior angles of a triangle is 180. Theorem A1.2 The product of two even natural numbers is even. Theorem A1.3 The product of any three consecutive even natural numbers is divisible by 16. A conjecture is a statement which we believe is true, based on our mathematical understanding and experience, that is, our mathematical intuition. The conjecture may turn out to be true or false. If we can prove it, then it becomes a theorem. Mathematicians often come up with conjectures by looking for patterns and making intelligent mathematical guesses. Let us look at some patterns and see what kind of intelligent guesses we can make. Example 4 Take any three consecutive even numbers and add them, say, 2 4 6 12, 4 6 8 18, 6 8 10 24, 8 10 12 30, 20 22 24 66. Is there any pattern you can guess in these sums? What can you conjecture about them? Solution One conjecture could be (i) the sum of three consecutive even numbers is even. Another could be (ii) the sum of three consecutive even numbers is divisible by 6. 2019-2020

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Lincoln to us Democracy is government of the people, by the people and for the people. We in Meghalaya always ruled ourselves. That is accepted by everyone. Why do we need to change that? Lyngdoh Madam I am not saying we need to change it. I too find this definition very beautiful. 2019-20

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India and the Contemporary World 130 Fig. 2 A Strangers Home, The Illustrated London News,1870. Night Refuges and Strangers Homes were opened in winter by charitable societies and local authorities in many towns. The poor flocked to these places in the hope of food, warmth and shelter. Imagine that you are a newspaper reporter writing a piece on the changes you see in London in 1811. What problems are you likely to write about? Who would have gained from the changes? Activity women, many of them recent migrants. A large number of women used their homes to increase family income by taking in lodgers or through such activities as tailoring, washing or matchbox making. However, there was a change once again in the twentieth century. As women got employment in wartime industries and offices, they withdrew from domestic service. Large number of children were pushed into low-paid work, often by their parents. Andrew Mearns, a clergyman who wrote The Bitter Cry of Outcast London in the 1880s, showed why crime was more profitable than labouring in small underpaid factories A child seven years old is easily known to make 10 shillings 6 pence a week from thieving Before he can gain as much as the young thief a boy must make 56 gross of matchboxes a week, or 1,296 a day. It was only after the passage of the Compulsory Elementary Education Act in 1870, and the factory acts beginning from 1902, that children were kept out of industrial work. 1.3 Housing Older cities like London changed dramatically when people began pouring in after the Industrial Revolution. Factory or workshop 2018-19

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Nazism and the Rise of Hitler 49 In the spring of 1945, a little eleven-year-old German boy called Helmuth was lying in bed when he overheard his parents discussing something in serious tones. His father, a prominent physician, deliberated with his wife whether the time had come to kill the entire family, or if he should commit suicide alone. His father spoke about his fear of revenge, saying, Now the Allies will do to us what we did to the crippled and Jews. The next day, he took Helmuth to the woods, where they spent their last happy time together, singing old childrens songs. Later, Helmuths father shot himself in his office. Helmuth remembers that he saw his fathers bloody uniform being burnt in the family fireplace. So traumatised was he by what he had overheard and what had happened, that he reacted by refusing to eat at home for the following nine years! He was afraid that his mother might poison him. Although Helmuth may not have realised all that it meant, his father had been a Nazi and a supporter of Adolf Hitler. Many of you will know something about the Nazis and Hitler. You probably know of Hitlers determination to make Germany into a mighty power and his ambition of conquering all of Europe. You may have heard that he killed Jews. But Nazism was not one or two isolated acts. It was a system, a structure of ideas about the world and politics. Let us try and understand what Nazism was all about. Let us see why Helmuths father killed himself and what the basis of his fear was. In May 1945, Germany surrendered to the Allies. Anticipating what was coming, Hitler, his propaganda minister Goebbels and his entire family committed suicide collectively in his Berlin bunker in April. At the end of the war, an International Military Tribunal at Nuremberg was set up to prosecute Nazi war criminals for Crimes against Peace, for War Crimes and Crimes Against Humanity. Germanys conduct during the war, especially those actions which Nazism and the Rise Nazism and the Rise Nazism and the Rise Nazism and the Rise Nazism and the Rise of Hitler of Hitler of Hitler of Hitler of Hitler Nazism and the Rise of Hitler Fig.1 Hitler (centre) and Goebbels (left) leaving after an official meeting, 1932. New words Allies The Allied Powers were initially led by the UK and France. In 1941 they were joined by the USSR and USA. They fought against the Axis Powers, namely Germany, Italy and Japan. Chapter III 2019-2020

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158 MATHEMATICS Let us now take some examples to illustrate the use of the above theorem. Example 1 In Fig. 9.13, ABCD is a parallelogram and EFCD is a rectangle. Also, AL DC. Prove that (i) ar (ABCD) ar (EFCD) (ii) ar (ABCD) DC AL Solution (i) As a rectangle is also a parallelogram, therefore, ar (ABCD) ar (EFCD) (Theorem 9.1) (ii) From above result, ar (ABCD) DC FC (Area of the rectangle length breadth) (1) As AL DC, therefore, AFCL is also a rectangle So, AL FC (2) Therefore, ar (ABCD) DC AL From (1) and (2) Can you see from the Result (ii) above that area of a parallelogram is the product of its any side and the coresponding altitude. Do you remember that you have studied this formula for area of a parallelogram in Class VII. On the basis of this formula, Theorem 9.1 can be rewritten as parallelograms on the same base or equal bases and between the same parallels are equal in area. Can you write the converse of the above statement? It is as follows Parallelograms on the same base (or equal bases) and having equal areas lie between the same parallels. Is the converse true? Prove the converse using the formula for area of the parallelogram. Example 2 If a triangle and a parallelogram are on the same base and between the same parallels, then prove that the area of the triangle is equal to half the area of the parallelogram. Solution Let ABP and parallelogram ABCD be on the same base AB and between the same parallels AB and PC (see Fig. 9.14). You wish to prove that ar (PAB) 1 ar(ABCD) 2 Draw BQ AP to obtain another parallelogram ABQP. Now parallelograms ABQP and ABCD are on the same base AB and between the same parallels AB and PC. Fig. 9.13 Fig. 9.14 2019-2020

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Gender, Religion and Caste 41 their educational and career opportunities. More radical womens movements aimed at equality in personal and family life as well. These movements are called FEMINIST movements. Political expression of gender division and political mobilisation on this Discuss all these perceptions of an ideal woman that prevail in our society. Do you agree with any of these? If not, what is your image of an ideal woman? Feminist A woman or a man who believes in equal rights and opportunities for women and men. Zuban question helped to improve womens role in public life. We now find women working as scientists, doctors, engineers, lawyers, managers and college and university teachers which were earlier not considered suitable for women. In some parts of the world, for example in 2018-19

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150 MATHEMATICS Similarly, from OQD, OD2 OQ2 DQ2 (2) From OQC, we have OC2 OQ2 CQ2 (3) and from OAP, we have OA2 AP2 OP2 (4) Adding (1) and (2), OB2 OD2 BP2 OP2 OQ2 DQ2 CQ2 OP2 OQ2 AP2 (As BP CQ and DQ AP) CQ2 OQ2 OP2 AP2 OC2 OA2 From (3) and (4) EXERCISE 6.5 1. Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse. (i) 7 cm, 24 cm, 25 cm (ii) 3 cm, 8 cm, 6 cm (iii) 50 cm, 80 cm, 100 cm (iv) 13 cm, 12 cm, 5 cm 2. PQR is a triangle right angled at P and M is a point on QR such that PM QR. Show that PM2 QM . MR. 3. In Fig. 6.53, ABD is a triangle right angled at A and AC BD. Show that (i) AB2 BC . BD (ii) AC2 BC . DC (iii) AD2 BD . CD 4. ABC is an isosceles triangle right angled at C. Prove that AB2 2AC2. 5. ABC is an isosceles triangle with AC BC. If AB2 2 AC2, prove that ABC is a right triangle. 6. ABC is an equilateral triangle of side 2a. Find each of its altitudes. 7. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals. Fig. 6.53 2019-20

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Poverty as a Challenge 29 Overview This chapter deals with one of the most difficult challenges faced by independent Indiapoverty. After discussing this multi-dimensional problem through examples, the chapter discusses the way poverty is seen in social sciences. Poverty trends in India and the world are illustrated through the concept of the poverty line. Causes of poverty as well as anti-poverty measures taken by the government are also discussed. The chapter ends with broadening the official concept of poverty into human poverty. Introduction In our daily life, we come across many people who we think are poor. They could be landless labourers in villages or people living in overcrowded jhuggis in cities. They could be daily wage workers at construction sites or child workers in Poverty as a Challenge Chapter dhabas. They could also be beggars with children in tatters. We see poverty all around us. In fact, every fourth person in India is poor. This means, roughly 270 million (or 27 crore) people in India live in poverty 2011-12. This also means that India has the largest single concentration of the poor in the world. This illustrates the seriousness of the challenge. Two Typical Cases of Poverty Urban Case Thirty-three year old Ram Saran works as a daily-wage labourer in a wheat flour mill near Ranchi in Jharkhand. He manages to earn around Rs 1,500 a month when he finds employment, which is not often. The money is not enough to sustain his family of six that includes his wife and four children aged between 12 years to six months. Poverty as a Challenge 33 Picture 3.1 Story of Ram Saran 2019-2020

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NATURAL RESOURCES 201 Activity 14.13 Find out which other molecules are thought to damage the ozone layer. Newspaper reports often talk about the hole in the ozone layer. Find out whether the size of this hole is changing and in what manner scientists think this would affect life on Earth (Fig. 14.9). Q What you have learnt Life on Earth depends on resources like soil, water and air, and energy from the Sun. Uneven heating of air over land and water-bodies causes winds. Evaporation of water from water-bodies and subsequent condensation give us rain. Rainfall patterns depend on the prevailing wind patterns in an area. Various nutrients are used again and again in a cyclic fashion. This leads to a certain balance between the various components of the biosphere. Pollution of air, water and soil affect the quality of life and harm the biodiversity. We need to conserve our natural resources and use them in a sustainable manner. Exercises 1. Why is the atmosphere essential for life? 2. Why is water essential for life? 3. How are living organisms dependent on the soil? Are organisms that live in water totally independent of soil as a resource? 4. You have seen weather reports on television and in newspapers. How do you think we are able to predict the weather? uestions 1. What are the different states in which water is found during the water cycle? 2. Name two biologically important compounds that contain both oxygen and nitrogen. 3. List any three human activities which would lead to an increase in the carbon dioxide content of air. 4. What is the greenhouse effect? 5. What are the two forms of oxygen found in the atmosphere? 2019-2020

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Forest Society and Colonialism 95 4.4 War and Deforestation The First World War and the Second World War had a major impact on forests. In India, working plans were abandoned at this time, and the forest department cut trees freely to meet British war needs. In Java, just before the Japanese occupied the region, the Dutch followed a scorched earth policy, destroying sawmills, and burning huge piles of giant teak logs so that they would not fall into Japanese hands. The Japanese then exploited the forests recklessly for their own war industries, forcing forest villagers to cut down forests. Many villagers used this opportunity to expand cultivation in the forest. After the war, it was difficult for the Indonesian forest service to get this land back. As in India, peoples need for agricultural land has brought them into conflict with the forest departments desire to control the land and exclude people from it. 4.5 New Developments in Forestry Since the 1980s, governments across Asia and Africa have begun to see that scientific forestry and the policy of keeping forest communities away from forests has resulted in many conflicts. Conservation of forests rather than collecting timber has become a more important goal. The government has recognised that in order to meet this goal, the people who live near the forests must be involved. In many cases, across India, from Mizoram to Kerala, dense forests have survived only because villages protected them in sacred groves known as sarnas, devarakudu, kan, rai, etc. Some villages have been patrolling their own forests, with each household taking it in turns, instead of leaving it to the forest guards. Local forest communities and environmentalists today are thinking of different forms of forest management. Fig.23 Indian Munitions Board, War Timber Sleepers piled at Soolay pagoda ready for shipment,1917. The Allies would not have been as successful in the First World War and the Second World War if they had not been able to exploit the resources and people of their colonies. Both the world wars had a devastating effect on the forests of India, Indonesia and elsewhere. The forest department cut freely to satisfy war needs. Fig.24 Log yard in Rembang under Dutch colonial rule. 2019-2020

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33 Nehru Memorial Museum and Library, New Delhi 2019-20

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The Story of Village Palampur 7 Lets Discuss In the Picture 1.5, can you shade the land cultivated by the small farmers? Why do so many families of farmers cultivate such small plots of land? The distribution of farmers in India and the amount of land they cultivate is given in the following Graph 1.1. Discuss in the classroom. Graph 1.1 Distribution of Cultivated Area and Farmers Lets Discuss Would you agree that the distribution of cultivated land is unequal in Palampur? Do you find a similar situation for India? Explain. 5. Who will provide the labour? After land, labour is the next necessary factor for production. Farming requires a great deal of hard work. Small farmers along with their families cultivate their own fields. Thus, they provide the labour required for farming themselves. Medium and large farmers hire farm labourers to work on their fields. Lets Discuss Identify the work being done on the field in the Pictures 1.6 and arrange them in a proper sequence. Farm labourers come either from landless families or families cultivating small plots of land. Unlike farmers, farm labourers do not have a right over the Picture 1.6 Work on the fields Wheat crop ploughing by bullocks, sowing, spraying of insecticides, cultivation by traditional method, cultivation by modern method, and cutting of crops. Source Pocket Book of Agriculture Statistics 2017 and State of Indian Agriculture 2017, Department of Agriculture, Cooperation and Farmers Welfare (As per Agriculture Census, 2010 11). 2019-2020

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250 MATHEMATICS Let us represent the data given above graphically as follows (i) We represent the weights on the horizontal axis on a suitable scale. We can choose the scale as 1 cm 5 kg. Also, since the first class interval is starting from 30.5 and not zero, we show it on the graph by marking a kink or a break on the axis. (ii) We represent the number of students (frequency) on the vertical axis on a suitable scale. Since the maximum frequency is 15, we need to choose the scale to accomodate this maximum frequency. (iii) We now draw rectangles (or rectangular bars) of width equal to the class-size and lengths according to the frequencies of the corresponding class intervals. For example, the rectangle for the class interval 30.5 - 35.5 will be of width 1 cm and length 4.5 cm. (iv) In this way, we obtain the graph as shown in Fig. 14.3 Fig. 14.3 Observe that since there are no gaps in between consecutive rectangles, the resultant graph appears like a solid figure. This is called a histogram, which is a graphical representation of a grouped frequency distribution with continuous classes. Also, unlike a bar graph, the width of the bar plays a significant role in its construction. Here, in fact, areas of the rectangles erected are proportional to the corresponding frequencies. However, since the widths of the rectangles are all equal, the lengths of the rectangles are proportional to the frequencies. That is why, we draw the lengths according to (iii) above. 2019-2020

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Magnetic Effects of Electric Current We know that the magnetic field produced by a current-carrying wire at a given point depends directly on the current passing through it. Therefore, if there is a circular coil having n turns, the field produced is n times as large as that produced by a single turn. This is because the current in each circular turn has the same direction, and the field due to each turn then just adds up. Take a rectangular cardboard having two holes. Insert a circular coil having large number of turns through them, normal to the plane of the cardboard. Connect the ends of the coil in series with a battery, a key and a rheostat, as shown in Fig. 13.9. Sprinkle iron filings uniformly on the cardboard. Plug the key. Tap the cardboard gently a few times. Note the pattern of the iron filings that emerges on the cardboard. Figure 13.9 Figure 13.9 Figure 13.9 Figure 13.9 Figure 13.9 Magnetic field produced by a current- carrying circular coil. A coil of many circular turns of insulated copper wire wrapped closely in the shape of a cylinder is called a solenoid. The pattern of the magnetic field lines around a current-carrying solenoid is shown in Fig. 13.10. Compare the pattern of the field with the magnetic field around a bar magnet (Fig. 13.4). Do they look similar? Yes, they are similar. In fact, one end of the solenoid behaves as a magnetic north pole, while the other behaves as the south pole. The field lines inside the solenoid are in the form of parallel straight lines. This indicates that the magnetic field is the same at all points inside the solenoid. That is, the field is uniform inside the solenoid. A strong magnetic field produced inside a solenoid can be used to magnetise a piece of magnetic material, like soft iron, when placed inside the coil (Fig. 13.11). The magnet so formed is called an electromagnet. Figure 13.10 Figure 13.10 Figure 13.10 Figure 13.10 Figure 13.10 Field lines of the magnetic field through and around a current carrying solenoid. Figure 13.11 Figure 13.11 Figure 13.11 Figure 13.11 Figure 13.11 A current-carrying solenoid coil is used to magnetise steel rod inside it an electromagnet. 1. Consider a circular loop of wire lying in the plane of the table. Let the current pass through the loop clockwise. Apply the right-hand rule to find out the direction of the magnetic field inside and outside the loop. 2. The magnetic field in a given region is uniform. Draw a diagram to represent it. 2019-20

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SCIENCE 62 Was there a darkly coloured, spherical or oval, dot-like structure near the centre of each cell? This structure is called nucleus. Were there similar structures in onion peel cells? The nucleus has a double layered covering called nuclear membrane. The nuclear membrane has pores which allow the transfer of material from inside the nucleus to its outside, that is, to the cytoplasm (which we will talk about in section 5.2.4). The nucleus contains chromosomes, which are visible as rod-shaped structures only when the cell is about to divide. Chromosomes contain information for inheritance of characters from parents to next generation in the form of DNA (Deoxyribo Nucleic Acid) molecules. Chromosomes are composed of DNA and protein. DNA molecules contain the information necessary for constructing and organising cells. Functional segments of DNA are called genes. In a cell which is not dividing, this DNA is present as part of chromatin material. Chromatin material is visible as entangled mass of thread like structures. Whenever the cell is about to divide, the chromatin material gets organised into chromosomes. The nucleus plays a central role in cellular reproduction, the process by which a single cell divides and forms two new cells. It also plays a crucial part, along with the environment, in determining the way the cell will develop and what form it will exhibit at maturity, by directing the chemical activities of the cell. In some organisms like bacteria, the nuclear region of the cell may be poorly defined due to the absence of a nuclear membrane. Such an undefined nuclear region containing only nucleic acids is called a nucleoid. Such organisms, whose cells lack a nuclear membrane, are called prokaryotes (Pro primitive or primary karyote karyon nucleus). Organisms with cells having a nuclear membrane are called eukaryotes. Prokaryotic cells (see Fig. 5.4) also lack most of the other cytoplasmic organelles present in eukaryotic cells. Many of the functions of such organelles are also performed by poorly organised parts of the cytoplasm (see section 5.2.4). The chlorophyll in photosynthetic prokaryotic bacteria is associated with membranous vesicles (bag like structures) but not with plastids as in eukaryotic cells (see section 5.2.5). Ribosomes Plasma membrane Cell wall Nucleoid Fig. 5.4 Prokaryotic cell 5.2.4 CYTOPLASM When we look at the temporary mounts of onion peel as well as human cheek cells, we can see a large region of each cell enclosed by the cell membrane. This region takes up very little stain. It is called the cytoplasm. The cytoplasm is the fluid content inside the plasma membrane. It also contains many specialised cell organelles. Each of these organelles performs a specific function for the cell. Cell organelles are enclosed by membranes. In prokaryotes, beside the absence of a defined nuclear region, the membrane-bound cell organelles are also absent. On the other hand, the eukaryotic cells have nuclear membrane as well as membrane-enclosed organelles. The significance of membranes can be illustrated with the example of viruses. Viruses lack any membranes and hence do not show characteristics of life until they enter a living body and use its cell machinery to multiply. 2019-2020

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PAIR OF LINEAR EQUATIONS IN TWO VARIABLES 61 Then (3)( 74) (5)( 46) x 1 ( 46)(3) ( 74)(2) (2)(5) (3)(3) y i.e., 222 230 x 1 138 148 10 9 y i.e., 8 x 1 10 1 y i.e., 8 x 1 1 and 10 y 1 1 i.e., x 8 and y 10 Hence, the fare from the bus stand in Bangalore to Malleswaram is 8 and the fare to Yeshwanthpur is 10. Verification You can check from the problem that the solution we have got is correct. Example 15 For which values of p does the pair of equations given below has unique solution? 4x py 8 0 2x 2y 2 0 Solution Here a1 4, a2 2, b1 p, b2 2. Now for the given pair to have a unique solution 1 2 a a 1 2 b b i.e., 4 2 2 p i.e., p 4 Therefore, for all values of p, except 4, the given pair of equations will have a unique solution. Example 16 For what values of k will the following pair of linear equations have infinitely many solutions? kx 3y (k 3) 0 12x ky k 0 Solution Here, 1 1 1 2 2 2 3 3 , , 12 a b c k k a b k c k For a pair of linear equations to have infinitely many solutions 1 1 1 2 2 2 a b c a b c 2019-20

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118 MATHEMATICS Observe that the triangles may or may not be congruent to each other. So, equality of three angles is not sufficient for congruence of triangles. Therefore, for congruence of triangles out of three equal parts, one has to be a side. Let us now take some more examples. Example 3 Line-segment AB is parallel to another line-segment CD. O is the mid-point of AD (see Fig. 7.15). Show that (i) AOB DOC (ii) O is also the mid-point of BC. Solution (i) Consider AOB and DOC. ABO DCO (Alternate angles as AB CD and BC is the transversal) AOB DOC (Vertically opposite angles) OA OD (Given) Therefore, AOB DOC (AAS rule) (ii) OB OC (CPCT) So, O is the mid-point of BC. EXERCISE 7.1 1. In quadrilateral ACBD, AC AD and AB bisects A (see Fig. 7.16). Show that ABC ABD. What can you say about BC and BD? Fig. 7.15 Fig. 7.16 2019-2020

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India and the Contemporary World 48 In earlier times, foreign travellers in India marvelled at the courage, truthfulness and modesty of the people of the Arya vamsa now they remark mainly on the absence of those qualities. In those days Hindus would set out on conquest and hoist their flags in Tartar, China and other countries now a few soldiers from a tiny island far away are lording it over the land of India. Tarinicharan Chattopadhyay, Bharatbarsher Itihas (The History of Bharatbarsh), vol. 1, 1858. Source E Source revival. In Madras, Natesa Sastri published a massive four-volume collection of Tamil folk tales, The Folklore of Southern India. He believed that folklore was national literature it was the most trustworthy manifestation of peoples real thoughts and characteristics. As the national movement developed, nationalist leaders became more and more aware of such icons and symbols in unifying people and inspiring in them a feeling of nationalism. During the Swadeshi movement in Bengal, a tricolour flag (red, green and yellow) was designed. It had eight lotuses representing eight provinces of British India, and a crescent moon, representing Hindus and Muslims. By 1921, Gandhiji had designed the Swaraj flag. It was again a tricolour (red, green and white) and had a spinning wheel in the centre, representing the Gandhian ideal of self-help. Carrying the flag, holding it aloft, during marches became a symbol of defiance. Another means of creating a feeling of nationalism was through reinterpretation of history. By the end of the nineteenth century many Indians began feeling that to instill a sense of pride in the nation, Indian history had to be thought about differently. The British saw Indians as backward and primitive, incapable of governing themselves. In response, Indians began looking into the past to discover Indias great achievements. They wrote about the glorious developments in ancient times when art and architecture, science and mathematics, religion and culture, law and philosophy, crafts and trade had flourished. This glorious time, in their view, was followed by a history of decline, when India was colonised. These nationalist histories urged the readers to take pride in Indias great achievements in the past and struggle to change the miserable conditions of life under British rule. These efforts to unify people were not without problems. When the past being glorified was Hindu, when the images celebrated were drawn from Hindu iconography, then people of other communities felt left out. Fig. 14a Bharat Mata. This figure of Bharat Mata is a contrast to the one painted by Abanindranath Tagore. Here she is shown with a trishul, standing beside a lion and an elephant both symbols of power and authority. Look at Figs. 12 and 14. Do you think these images will appeal to all castes and communities? Explain your views briefly. Activity 2019-20

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192 India and the Contemporary World The most popular historical novelist in Tamil was R. Krishnamurthy who wrote under the pen- name Kalki. He was an active participant in the freedom movement and the editor of the widely read Tamil magazines Anandavikatan and Kalki. Written in simple language and full of heroism, adventure and suspense, Kalkis novels captivated the Tamil-reading public of an entire generation. Box 7 Fig. 19 A page from the novel Ponniyin Selvan, written by Kalki and serialised in the magazine Kalki, 1951. world of print for the first time. The way characters spoke in a novel began to indicate their region, class or caste. Thus novels made their readers familiar with the ways in which people in other parts of their land spoke their language. 3.2 The Problem of Being Modern Although they were about imaginary stories, novels often spoke to their readers about the real world. But novels did not always show things exactly as they were in reality. Sometimes, they presented a vision of how things ought to be. Social novelists often created heroes and heroines with ideal qualities, who their readers could admire and imitate. How were these ideal qualities defined? In many novels written during the colonial period, the ideal person successfully deals with one of the central dilemmas faced by colonial subjects how to be modern without rejecting tradition, how to accept ideas coming from the West without losing ones identity. Chandu Menon portrayed Indulekha as a woman of breathtaking beauty, high intellectual abilities, artistic talent, and with an education in English and Sanskrit. Madhavan, the hero of the novel, was also presented in ideal colours. He was a member of the newly English-educated class of Nayars from the University of Madras. 2018-19

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228 MATHEMATICS Let us now take some examples to understand these concepts (or results). Example 2 Find the area of the sector of a circle with radius 4 cm and of angle 30. Also, find the area of the corresponding major sector (Use 3.14). Solution Given sector is OAPB (see Fig. 12.8). Area of the sector 2 360 r 2 30 3.14 4 4 cm 360 2 2 12.56 cm 4.19cm 3 (approx.) Area of the corresponding major sector r2 area of sector OAPB (3.14 16 4.19) cm2 46.05 cm2 46.1 cm2(approx.) Alternatively, area of the major sector 2 (360 ) 360 r 2 360 30 3.14 16 cm 360 2 2 330 3.14 16cm 46.05 cm 360 46.1 cm2 (approx.) Example 3 Find the area of the segment AYB shown in Fig. 12.9, if radius of the circle is 21 cm and AOB 120. (Use 22 7 ) Fig. 12.9 Fig. 12.8 2019-20

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LINEAR EQUATIONS IN TWO VARIABLES 67 While solving an equation, you must always keep the following points in mind The solution of a linear equation is not affected when (i) the same number is added to (or subtracted from) both the sides of the equation. (ii) you multiply or divide both the sides of the equation by the same non-zero number. Let us now consider the following situation In a One-day International Cricket match between India and Sri Lanka played in Nagpur, two Indian batsmen together scored 176 runs. Express this information in the form of an equation. Here, you can see that the score of neither of them is known, i.e., there are two unknown quantities. Let us use x and y to denote them. So, the number of runs scored by one of the batsmen is x, and the number of runs scored by the other is y. We know that x y 176, which is the required equation. This is an example of a linear equation in two variables. It is customary to denote the variables in such equations by x and y, but other letters may also be used. Some examples of linear equations in two variables are 1.2s 3t 5, p 4q 7, u 5v 9 and 3 2 x 7y. Note that you can put these equations in the form 1.2s 3t 5 0, p 4q 7 0, u 5v 9 0 and 2 x 7y 3 0, respectively. So, any equation which can be put in the form ax by c 0, where a, b and c are real numbers, and a and b are not both zero, is called a linear equation in two variables. This means that you can think of many many such equations. Example 1 Write each of the following equations in the form ax by c 0 and indicate the values of a, b and c in each case (i) 2x 3y 4.37 (ii) x 4 3 y (iii) 4 5x 3y (iv) 2x y Solution (i) 2x 3y 4.37 can be written as 2x 3y 4.37 0. Here a 2, b 3 and c 4.37. (ii) The equation x 4 3 y can be written as x 3 y 4 0. Here a 1, b 3 and c 4. (iii) The equation 4 5x 3y can be written as 5x 3y 4 0. Here a 5, b 3 and c 4. Do you agree that it can also be written as 5x 3y 4 0 ? In this case a 5, b 3 and c 4. 2019-2020

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India and the Contemporary World 166 5.2 Further Innovations By the late eighteenth century, the press came to be made out of metal. Through the nineteenth century, there were a series of further innovations in printing technology. By the mid-nineteenth century, Richard M. Hoe of New York had perfected the power-driven cylindrical press. This was capable of printing 8,000 sheets per hour. This press was particularly useful for printing newspapers. In the late nineteenth century, the offset press was developed which could print up to six colours at a time. From the turn of the twentieth century, electrically operated presses accelerated printing operations. A series of other developments followed. Methods of feeding paper improved, the quality of plates became better, automatic paper reels and photoelectric controls of the colour register were introduced. The accumulation of several individual mechanical improvements transformed the appearance of printed texts. Printers and publishers continuously developed new strategies to sell their product. Nineteenth-century periodicals serialised important novels, which gave birth to a particular way of writing novels. In the 1920s in England, popular works were sold in cheap series, called the Shilling Series. The dust cover or the book jacket is also a twentieth-century innovation. With the onset of the Great Depression in the 1930s, publishers feared a decline in book purchases. To sustain buying, they brought out cheap paperback editions. Look at Fig. 13. What impact do such advertisements have on the public mind? Do you think everyone reacts to printed material in the same way? Activity Fig. 13 Advertisements at a railway station in England, a lithograph by Alfred Concanen, 1874. Printed advertisements and notices were plastered on street walls, railway platforms and public buildings. 2018-19

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STRUCTURE OF THE ATOM 53 Q Many elements consist of a mixture of isotopes. Each isotope of an element is a pure substance. The chemical properties of isotopes are similar but their physical properties are different. Chlorine occurs in nature in two isotopic forms, with masses 35 u and 37 u in the ratio of 31. Obviously, the question arises what should we take as the mass of chlorine atom? Let us find out. The average atomic mass of chlorine atom, on the basis of above data, will be 35 75 100 37 25 100 105 4 37 4 142 4 35 5 . u The mass of an atom of any natural element is taken as the average mass of all the naturally occuring atoms of that element. If an element has no isotopes, then the mass of its atom would be the same as the sum of protons and neutrons in it. But if an element occurs in isotopic forms, then we have to know the percentage of each isotopic form and then the average mass is calculated. This does not mean that any one atom of chlorine has a fractional mass of 35.5 u. It means that if you take a certain amount of chlorine, it will contain both isotopes of chlorine and the average mass is 35.5 u. Applications Since the chemical properties of all the isotopes of an element are the same, normally we are not concerned about taking a mixture. But some isotopes have special properties which find them useful in various fields. Some of them are (i) An isotope of uranium is used as a fuel in nuclear reactors. (ii) An isotope of cobalt is used in the treatment of cancer. (iii) An isotope of iodine is used in the treatment of goitre. 4.6.1 ISOBARS Let us consider two elements calcium, atomic number 20, and argon, atomic number 18. The number of protons in these atoms is different, but the mass number of both these elements is 40. That is, the total number of nucleons is the same in the atoms of this pair of elements. Atoms of different elements with different atomic numbers, which have the same mass number, are known as isobars. uestions 1. For the symbol H,D and T tabulate three sub-atomic particles found in each of them. 2. Write the electronic configuration of any one pair of isotopes and isobars. What you have learnt Credit for the discovery of electron and proton goes to J.J. Thomson and E.Goldstein, respectively. J.J. Thomson proposed that electrons are embedded in a positive sphere. 2019-2020

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185 Novels, Society and History Women novelists George Eliot (1819-1880) was the pen-name of Mary Ann Evans. A very popular novelist, she believed that novels gave women a special opportunity to express themselves freely. Every woman could see herself as capable of writing fiction Fiction is a department of literature in which women can, after their kind, fully equal men No educational restrictions can shut women from the materials of fiction, and there is no species of art that is so free from rigid requirements. George Eliot, Silly novels by lady novelists, 1856. Box 1 1.5 Novels for the Young Novels for young boys idealised a new type of man someone who was powerful, assertive, independent and daring. Most of these novels were full of adventure set in places remote from Europe. The colonisers appear heroic and honourable confronting native peoples and strange surroundings, adapting to native life as well as changing it, colonising territories and then developing nations there. Books like R.L. Stevensons Treasure Island (1883) or Rudyard Kiplings Jungle Book (1894) became great hits. G.A. Hentys historical adventure novels for boys were also wildly popular during the height of the British empire. They aroused the excitement and adventure of conquering strange lands. They were set in Mexico, Alexandria, Siberia and many other countries. They were always about young boys who witness grand historical events, get involved in some military action and show what they called English courage. Love stories written for adolescent girls also first became popular in this period, especially in the US, notably Ramona (1884) by Helen Hunt Jackson and a series entitled What Katy Did (1872) by Sarah Chauncey Woolsey, who wrote under the pen-name Susan Coolidge. G.A. Henty (1832-1902) In Under Drakes Flag (1883) two young Elizabethan adventurers face their apparently approaching death, but still remember to assert their Englishness Well, Ned, we have had more good fortune than we could have expected. We might have been killed on the day when we landed, and we have spent six jolly months in wandering together as hunters on the plain. If we must die, let us behave like Englishmen and Christians. Box 2 Fig. 13 Charlotte Bronte (1816-1855). Aunt who is always unkind to her People think you a good woman, but you are bad ... You are deceitful! I will never call you aunt as long as I live. 2018-19

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SCIENCE 152 uestions 1. What is the kinetic energy of an object? 2. Write an expression for the kinetic energy of an object. 3. The kinetic energy of an object of mass, m moving with a velocity of 5 m s1 is 25 J. What will be its kinetic energy when its velocity is doubled? What will be its kinetic energy when its velocity is increased three times? 11.2.3 POTENTIAL ENERGY Activity 11.8 Take a rubber band. Hold it at one end and pull from the other. The band stretches. Release the band at one of the ends. What happens? The band will tend to regain its original length. Obviously the band had acquired energy in its stretched position. How did it acquire energy when stretched? Activity 11.9 Take a slinky as shown below. Ask a friend to hold one of its ends. You hold the other end and move away from your friend. Now you release the slinky. Activity 11.11 Lift an object through a certain height. The object can now do work. It begins to fall when released. This implies that it has acquired some energy. If raised to a greater height it can do more work and hence possesses more energy. From where did it get the energy? Think and discuss. In the above situations, the energy gets stored due to the work done on the object. The energy transferred to an object is stored as potential energy if it is not used to cause a change in the velocity or speed of the object. You transfer energy when you stretch a rubber band. The energy transferred to the band is its potential energy. You do work while winding the key of a toy car. The energy transferred to the spring inside is stored as potential energy. The potential energy possessed by the object is the energy present in it by virtue of its position or configuration. Activity 11.12 Take a bamboo stick and make a bow as shown in Fig. 11.6. Place an arrow made of a light stick on it with one end supported by the stretched string. Now stretch the string and release the arrow. Notice the arrow flying off the bow. Notice the change in the shape of the bow. The potential energy stored in the bow due to the change of shape is thus used in the form of kinetic energy in throwing off the arrow. Q Fig.11.6 An arrow and the stretched string on the bow. What happened? How did the slinky acquire energy when stretched? Would the slinky acquire energy when it is compressed? Activity 11.10 Take a toy car. Wind it using its key. Place the car on the ground. Did it move? From where did it acquire energy? Does the energy acquired depend on the number of windings? How can you test this? 2019-2020

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PROOFS IN MATHEMATICS 319 Number of points Number of regions 1 1 2 2 3 4 4 8 5 6 7 Some of you might have come up with a formula predicting the number of regions given the number of points. From Class IX, you may remember that this intelligent guess is called a conjecture. Suppose your conjecture is that given n points on a circle, there are 2n 1 mutually exclusive regions, created by joining the points with all possible lines. This seems an extremely sensible guess, and one can check that if n 5, we do get 16 regions. So, having verified this formula for 5 points, are you satisfied that for any n points there are 2n 1 regions? If so, how would you respond, if someone asked you, how you can be sure about this for n 25, say? To deal with such questions, you would need a proof which shows beyond doubt that this result is true, or a counter- example to show that this result fails for some n. Actually, if you are patient and try it out for n 6, you will find that there are 31 regions, and for n 7 there are 57 regions. So, n 6, is a counter-example to the conjecture above. This demonstrates the power of a counter-example. You may recall that in the Class IX we discussed that to disprove a statement, it is enough to come up with a single counter- example. You may have noticed that we insisted on a proof regarding the number of regions in spite of verifying the result for n 1, 2, 3, 4 and 5. Let us consider a few more examples. You are familiar with the following result (given in Chapter 5) 1 2 3 ... n ( 1) 2 n n . To establish its validity, it is not enough to verify the result for n 1, 2, 3, and so on, because there may be some n for which this result is not true (just as in the example above, the result failed for n 6). What we need is a proof which establishes its truth beyond doubt. You shall learn a proof for the same in higher classes. 2019-20

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Science 6. The position of three elements A, B and C in the Periodic Table are shown below Group 16 Group 17 - - - A - - B C (a) State whether A is a metal or non-metal. (b) State whether C is more reactive or less reactive than A. (c) Will C be larger or smaller in size than B? (d) Which type of ion, cation or anion, will be formed by element A? 7. Nitrogen (atomic number 7) and phosphorus (atomic number 15) belong to group 15 of the Periodic Table. Write the electronic configuration of these two elements. Which of these will be more electronegative? Why? 8. How does the electronic configuration of an atom relate to its position in the Modern Periodic Table? 9. In the Modern Periodic Table, calcium (atomic number 20) is surrounded by elements with atomic numbers 12, 19, 21 and 38. Which of these have physical and chemical properties resembling calcium? 10. Compare and contrast the arrangement of elements in Mendelevs Periodic Table and the Modern Periodic Table. I We have discussed the major attempts made for classifying elements. Find out (from the internet or library) about other attempts to classify elements. II We have studied the long form of the Periodic Table. The Modern Periodic Law has been used to arrange elements in other ways too. Find out what are these. 2019-20

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264 MATHEMATICS The third step is to find the product of di with the corresponding fi, and take the sum of all the fi dis. The calculations are shown in Table 14.4. Table 14.4 Class interval Number of Class mark di xi 47.5 fidi students ( fi) (xi) 10 - 25 2 17.5 30 60 25 - 40 3 32.5 15 45 40 - 55 7 47.5 0 0 55 - 70 6 62.5 15 90 70 - 85 6 77.5 30 180 85 - 100 6 92.5 45 270 Total fi 30 fidi 435 So, from Table 14.4, the mean of the deviations, d i i i f d f . Now, let us find the relation between d and x . Since in obtaining di, we subtracted a from each xi, so, in order to get the mean x , we need to add a to d . This can be explained mathematically as Mean of deviations, d i i i f d f So, d ( ) i i i f x a f i i i i i f x f a f f i i f x a f x a So, x a d i.e., x i i i f d a f 2019-20

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Socialism in Europe and the Russian Revolution 27 Almost all industries were the property of individuals. Liberals and radicals themselves were often property owners and employers. Having made their wealth through trade or industrial ventures, they felt that such effort should be encouraged that its benefits would be achieved if the workforce in the economy was healthy and citizens were educated. Opposed to the privileges the old aristocracy had by birth, they firmly believed in the value of individual effort, labour and enterprise. If freedom of individuals was ensured, if the poor could labour, and those with capital could operate without restraint, they believed that societies would develop. Many working men and women who wanted changes in the world rallied around liberal and radical groups and parties in the early nineteenth century. Some nationalists, liberals and radicals wanted revolutions to put an end to the kind of governments established in Europe in 1815. In France, Italy, Germany and Russia, they became revolutionaries and worked to overthrow existing monarchs. Nationalists talked of revolutions that would create nations where all citizens would have Fig.1 The London poor in the mid-nineteenth century as seen by a contemporary. From Henry Mayhew, London Labour and the London Poor, 1861. 2019-2020

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India and the Contemporary World 74 4 Rebuilding a World Economy The Post-war Era The Second World War broke out a mere two decades after the end of the First World War. It was fought between the Axis powers (mainly Nazi Germany, Japan and Italy) and the Allies (Britain, France, the Soviet Union and the US). It was a war waged for six years on many fronts, in many places, over land, on sea, in the air. Once again death and destruction was enormous. At least 60 million people, or about 3 per cent of the worlds 1939 population, are believed to have been killed, directly or indirectly, as a result of the war. Millions more were injured. Unlike in earlier wars, most of these deaths took place outside the battlefields. Many more civilians than soldiers died from war-related causes. Vast parts of Europe and Asia were devastated, and several cities were destroyed by aerial bombardment or relentless artillery attacks. The war caused an immense amount of economic devastation and social disruption. Reconstruction promised to be long and difficult. Two crucial influences shaped post-war reconstruction. The first was the USs emergence as the dominant economic, political and military power in the Western world. The second was the dominance of the Soviet Union. It had made huge sacrifices to defeat Nazi Germany, and transformed itself from a backward agricultural country into a world power during the very years when the capitalist world was trapped in the Great Depression. 4.1 Post-war Settlement and the Bretton Woods Institutions Economists and politicians drew two key lessons from inter-war economic experiences. First, an industrial society based on mass production cannot be sustained without mass consumption. But to ensure mass consumption, there was a need for high and stable incomes. Incomes could not be stable if employment was unstable. Thus stable incomes also required steady, full employment. But markets alone could not guarantee full employment. Therefore governments would have to step in to minimise Fig. 24 German forces attack Russia, July 1941. Hitlers attempt to invade Russia was a turning point in the war. Fig. 25 Stalingrad in Soviet Russia devastated by the war. 2019-20

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Science 4. Explain the nature of the covalent bond using the bond formation in CH3Cl. 5. Draw the electron dot structures for (a) ethanoic acid. (b) H2S. (c) propanone. (d) F2 . 6. What is an homologous series? Explain with an example. 7. How can ethanol and ethanoic acid be differentiated on the basis of their physical and chemical properties? 8. Why does micelle formation take place when soap is added to water? Will a micelle be formed in other solvents such as ethanol also? 9. Why are carbon and its compounds used as fuels for most applications? 10. Explain the formation of scum when hard water is treated with soap. 11. What change will you observe if you test soap with litmus paper (red and blue)? 12. What is hydrogenation? What is its industrial application? 13. Which of the following hydrocarbons undergo addition reactions C2H6, C3H8, C3H6, C2H2 and CH4. 14. Give a test that can be used to differentiate between saturated and unsaturated hydrocarbons. 15. Explain the mechanism of the cleaning action of soaps. I Use molecular model kits to make models of the compounds you have learnt in this Chapter. II Take about 20 mL of castor oilcotton seed oillinseed oilsoyabean oil in a beaker. Add 30 mL of 20 sodium hydroxide solution. Heat the mixture with continuous stirring for a few minutes till the mixture thickens. Add 5-10 g of common salt to this. Stir the mixture well and allow it to cool. You can cut out the soap in fancy shapes. You can also add perfume to the soap before it sets. 2019-20

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24 MATHEMATICS Case (i) Here, the graph cuts x-axis at two distinct points A and A. The x-coordinates of A and A are the two zeroes of the quadratic polynomial ax2 bx c in this case (see Fig. 2.3). Fig. 2.3 Case (ii) Here, the graph cuts the x-axis at exactly one point, i.e., at two coincident points. So, the two points A and A of Case (i) coincide here to become one point A (see Fig. 2.4). Fig. 2.4 The x-coordinate of A is the only zero for the quadratic polynomial ax2 bx c in this case. 2019-20

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320 MATHEMATICS Now, consider Fig. A1.3, where PQ and PR are tangents to the circle drawn from P. You have proved that PQ PR (Theorem 10.2). You were not satisfied by only drawing several such figures, measuring the lengths of the respective tangents, and verifying for yourselves that the result was true in each case. Do you remember what did the proof consist of ? It consisted of a sequence of statements (called valid arguments), each following from the earlier statements in the proof, or from previously proved (and known) results independent from the result to be proved, or from axioms, or from definitions, or from the assumptions you had made. And you concluded your proof with the statement PQ PR, i.e., the statement you wanted to prove. This is the way any proof is constructed. We shall now look at some examples and theorems and analyse their proofs to help us in getting a better understanding of how they are constructed. We begin by using the so-called direct or deductive method of proof. In this method, we make several statements. Each is based on previous statements. If each statement is logically correct (i.e., a valid argument), it leads to a logically correct conclusion. Example 10 The sum of two rational numbers is a rational number. Solution S.No. Statements AnalysisComments 1. Let x and y be rational numbers. Since the result is about rationals, we start with x and y which are rational. 2. Let m x n , n 0 and p y q , q 0 where m, n, p and q are integers. 3. So, m p mq np x y n q nq Fig. A1.3 Apply the definition of rationals. The result talks about the sum of rationals, so we look at x y. 2019-20

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REAL NUMBERS 3 moment we write down such equations we are using Euclids division lemma, which is given in Theorem 1.1. Getting back to our puzzle, do you have any idea how you will solve it? Yes! You must look for the multiples of 7 which satisfy all the conditions. By trial and error (using the concept of LCM), you will find he had 119 eggs. In order to get a feel for what Euclids division lemma is, consider the following pairs of integers 17, 6 5, 12 20, 4 Like we did in the example, we can write the following relations for each such pair 17 6 2 5 (6 goes into 17 twice and leaves a remainder 5) 5 12 0 5 (This relation holds since 12 is larger than 5) 20 4 5 0 (Here 4 goes into 20 five-times and leaves no remainder) That is, for each pair of positive integers a and b, we have found whole numbers q and r, satisfying the relation a bq r, 0 r b Note that q or r can also be zero. Why dont you now try finding integers q and r for the following pairs of positive integers a and b? (i) 10, 3 (ii) 4, 19 (iii) 81, 3 Did you notice that q and r are unique? These are the only integers satisfying the conditions a bq r, where 0 r b. You may have also realised that this is nothing but a restatement of the long division process you have been doing all these years, and that the integers q and r are called the quotient and remainder, respectively. A formal statement of this result is as follows Theorem 1.1 (Euclids Division Lemma) Given positive integers a and b, there exist unique integers q and r satisfying a bq r, 0 r b. This result was perhaps known for a long time, but was first recorded in Book VII of Euclids Elements. Euclids division algorithm is based on this lemma. 2019-20

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INTRODUCTION TO TRIGONOMETRY 173 8 There is perhaps nothing which so occupies the middle position of mathematics as trigonometry. J.F. Herbart (1890) 8.1 Introduction You have already studied about triangles, and in particular, right triangles, in your earlier classes. Let us take some examples from our surroundings where right triangles can be imagined to be formed. For instance 1. Suppose the students of a school are visiting Qutub Minar. Now, if a student is looking at the top of the Minar, a right triangle can be imagined to be made, as shown in Fig 8.1. Can the student find out the height of the Minar, without actually measuring it? 2. Suppose a girl is sitting on the balcony of her house located on the bank of a river. She is looking down at a flower pot placed on a stair of a temple situated nearby on the other bank of the river. A right triangle is imagined to be made in this situation as shown in Fig.8.2. If you know the height at which the person is sitting, can you find the width of the river? INTRODUCTION TO TRIGONOMETRY Fig. 8.1 Fig. 8.2 2019-20

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India and the Contemporary World 40 with the British, as they had done in 1921-22, but also to break colonial laws. Thousands in different parts of the country broke the salt law, manufactured salt and demonstrated in front of government salt factories. As the movement spread, foreign cloth was boycotted, and liquor shops were picketed. Peasants refused to pay revenue and chaukidari taxes, village officials resigned, and in many places forest people violated forest laws going into Reserved Forests to collect wood and graze cattle. Worried by the developments, the colonial government began arresting the Congress leaders one by one. This led to violent clashes in many palaces. When Abdul Ghaffar Khan, a devout disciple of Mahatma Gandhi, was arrested in April 1930, angry crowds demonstrated in the streets of Peshawar, facing armoured cars and police firing. Many were killed. A month later, when Mahatma Gandhi himself was arrested, industrial workers in Sholapur attacked police posts, municipal buildings, lawcourts and railway stations all structures that symbolised British rule. A frightened government responded with a policy of brutal repression. Peaceful satyagrahis were attacked, women and children were beaten, and about 100,000 people were arrested. In such a situation, Mahatma Gandhi once again decided to call off the movement and entered into a pact with Irwin on 5 March 1931. By this Gandhi-Irwin Pact, Gandhiji consented to participate in a Round Table Conference (the Congress had boycotted the first Fig. 7 The Dandi march. During the salt march Mahatma Gandhi was accompanied by 78 volunteers. On the way they were joined by thousands. Fig. 8 Police cracked down on satyagrahis, 1930. 2019-20

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LINEAR EQUATIONS IN TWO VARIABLES 71 In the previous chapter, you studied how to plot the points on a graph paper. Let us plot the points (0, 3), (2, 2), (4, 1) and (6, 0) on a graph paper. Now join any two of these points and obtain a line. Let us call this as line AB (see Fig. 4.2). Do you see that the other two points also lie on the line AB? Now, pick another point on this line, say (8, 1). Is this a solution? In fact, 8 2(1) 6. So, (8, 1) is a solution. Pick any other point on this line AB and verify whether its coordinates satisfy the equation or not. Now, take any point not lying on the line AB, say (2, 0). Do its coordinates satisfy the equation? Check, and see that they do not. Let us list our observations 1. Every point whose coordinates satisfy Equation (1) lies on the line AB. 2. Every point (a, b) on the line AB gives a solution x a, y b of Equation (1). 3. Any point, which does not lie on the line AB, is not a solution of Equation (1). So, you can conclude that every point on the line satisfies the equation of the line and every solution of the equation is a point on the line. In fact, a linear equation in two variables is represented geometrically by a line whose points make up the collection of solutions of the equation. This is called the graph of the linear equation. So, to obtain the graph of a linear equation in two variables, it is enough to plot two points corresponding to two solutions and join them by a line. However, it is advisable to plot more than two such points so that you can immediately check the correctness of the graph. Remark The reason that a, degree one, polynomial equation ax by c 0 is called a linear equation is that its geometrical representation is a straight line. Example 5 Given the point (1, 2), find the equation of a line on which it lies. How many such equations are there? Solution Here (1, 2) is a solution of a linear equation you are looking for. So, you are looking for any line passing through the point (1, 2). One example of such a linear equation is x y 3. Others are y x 1, y 2x, since they are also satisfied by the coordinates of the point (1, 2). In fact, there are infinitely many linear equations which Fig. 4.2 2019-2020

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Science Figure 13.20 gives a schematic diagram of one of the common domestic circuits. In each separate circuit, different appliances can be connected across the live and neutral wires. Each appliance has a separate switch to ONOFF the flow of current through it. In order that each appliance has equal potential difference, they are connected parallel to each other. Electric fuse is an important component of all domestic circuits. We have already studied the principle and working of a fuse in the previous chapter (see Section 12.7). A fuse in a circuit prevents damage to the appliances and the circuit due to overloading. Overloading can occur when the live wire and the neutral wire come into direct contact. (This occurs when the insulation of wires is damaged or there is a fault in the appliance.) In such a situation, the current in the circuit abruptly increases. This is called short-circuiting. The use of an electric fuse prevents the electric circuit and the appliance from a possible damage by stopping the flow of unduly high electric current. The Joule heating that takes place in the fuse melts it to break the electric circuit. Overloading can also occur due to an accidental hike in the supply voltage. Sometimes overloading is caused by connecting too many appliances to a single socket. Figure 13.20 Figure 13.20 Figure 13.20 Figure 13.20 Figure 13.20 A schematic diagram of one of the common domestic circuits 1. Name two safety measures commonly used in electric circuits and appliances. 2. An electric oven of 2 kW power rating is operated in a domestic electric circuit (220 V) that has a current rating of 5 A. What result do you expect? Explain. 3. What precaution should be taken to avoid the overloading of domestic electric circuits? 2019-20

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22 MATHEMATICS (iii) ( ) ( ) a b a b a b (iv) ( ) ( ) 2 a b a b a b (v) ( ) ( ) a b c d ac ad bc bd (vi) ( ) 2 2 a b a ab b Let us look at some particular cases of these identities. Example 16 Simplify the following expressions (i) ( ) ( ) 5 7 2 5 (ii) ( ) ( ) 5 5 5 5 (iii) ( ) 2 3 7 (iv) ( ) ( ) 11 7 11 7 Solution (i) ( ) ( ) 5 7 2 5 10 5 5 2 7 35 (ii) ( ) ( ) ( ) 2 2 5 5 5 5 5 5 25 5 20 (iii) ( ) ( ) ( ) 2 2 2 3 7 3 2 3 7 7 3 2 21 7 10 2 21 (iv) ( ) ( ) ( ) ( ) 2 2 11 7 11 7 11 7 11 7 4 Remark Note that simplify in the example above has been used to mean that the expression should be written as the sum of a rational and an irrational number. We end this section by considering the following problem. Look at 1 2 Can you tell where it shows up on the number line? You know that it is irrational. May be it is easier to handle if the denominator is a rational number. Let us see, if we can rationalise the denominator, that is, to make the denominator into a rational number. To do so, we need the identities involving square roots. Let us see how. Example 17 Rationalise the denominator of 1 2 Solution We want to write 1 2 as an equivalent expression in which the denominator is a rational number. We know that 2 . 2 is rational. We also know that multiplying 2019-2020

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Democracy and Diversity 31 The International Olympic Association held Carlos and Smith guilty of violating the Olympic spirit by making a political statement. Their medals were taken back. Back home, they were subjected to a lot of criticism. Norman too suffered for his action and was not included in the Australian team for the next Olympic. But their action succeeded in gaining international attention for the Civil Rights Movement in the US. Recently, the San Jose (pronounced Saan Hoze) State University, of which they were former students, honoured them and installed their statue in the University campus. When Norman died in 2006, Smith and Carlos were pallbearers at his funeral. Some Dalit groups decided to participate in the UN Conference Against Racism in Durban in 2001, demanding the inclusion of caste in the agenda of this conference. Here are three reactions to this move Amandeep Kaur (a government official) Our Constitution declares caste discrimination to be illegal. If some caste discrimination continues, it is an internal matter. I am opposed to this being raised in an international forum. Oinam (a sociologist) I am opposed to this because caste and race are not similar divisions. Caste is a social division, while race is a biological one. Raising caste in this conference on racism would mean equating the two. Ashok (a Dalit activist) The argument about internal matter is a way of preventing open discussion of oppression and discrimination. Race is not purely biological. It is as much a legal and sociological category as caste. Caste discrimination must be raised in this conference. Which of the three opinions do you agree with most and why? Differences, similarities, divisions The athletes in the example above were responding to social divisions and social inequalities. But does that happen only in societies which have racial divisions? In the previous two chapters we have already noted some other forms of social divisions. The examples of Belgium and Sri Lanka show both regional and social divisions. In the case of Belgium we noted that people who live in different regions speak different languages. In Sri Lanka, we noted linguistic as well as religious differences. Thus social diversity can take different forms in different societies. I met this group of girls from Pakistan and felt that I had more in common with them than many girls from other parts of my own country. Is this anti-national to feel so? 2018-19

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153 Print Culture It is difficult for us to imagine a world without printed matter. We find evidence of print everywhere around us in books, journals, newspapers, prints of famous paintings, and also in everyday things like theatre programmes, official circulars, calendars, diaries, advertisements, cinema posters at street corners. We read printed literature, see printed images, follow the news through newspapers, and track public debates that appear in print. We take for granted this world of print and often forget that there was a time before print. We may not realise that print itself has a history which has, in fact, shaped our contemporary world. What is this history? When did printed literature begin to circulate? How has it helped create the modern world? In this chapter we will look at the development of print, from its beginnings in East Asia to its expansion in Europe and in India. We will understand the impact of the spread of technology and consider how social lives and cultures changed with the coming of print. Print Culture a n d the Modern World Chapter VII Print Culture and the Modern World Fig. 1 Book making before the age of print, from Akhlaq-i-Nasiri, 1595. This is a royal workshop in the sixteenth century, much before printing began in India. You can see the text being dictated, written and illustrated. The art of writing and illustrating by hand was important in the age before print. Think about what happened to these forms of art with the coming of printing machines. 2018-19

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choose. There is no one to stop them from using unfair means to get their money back. Compared to the formal lenders, most of the informal lenders charge a much higher interest on loans. Thus, the cost to the borrower of informal loans is much higher. Higher cost of borrowing means a larger part of the earnings of the borrowers is used to repay the loan. Hence, borrowers have less income left for themselves (as we saw for Shyamal in Sonpur). In certain cases, the high interest rate for borrowing can mean that the amount to be repaid is greater than the income of the borrower. This could lead to increasing debt (as we saw for Rama in Sonpur) and debt trap. Also, people who might wish to start an enterprise by borrowing may not do so because of the high cost of borrowing. For these reasons, banks and cooperative societies need to lend more. This would lead to higher incomes and many people could then borrow cheaply for a variety of needs. They could grow crops, do business, set up small-scale industries etc. They could set up new industries or trade in goods. Cheap and affordable credit is crucial for the countrys develop- ment. Graph 2 shows the importance of formal and informal sources of credit for people in urban areas. The people are divided into four groups, from poor to rich, as shown in the figure. You can see that 85 per cent of the loans taken by poor households in the urban areas are from informal sources. Compare this with the rich urban households. What do you find? Only 10 per cent of their loans are from informal sources, while 90 per cent are from formal sources. A similar pattern is also found in rural areas. The rich households are availing cheap credit from formal lenders whereas the poor households have to pay a large amount for borrowing. What does all this suggest? First, the formal sector still meets only about half of the total credit needs of the rural people. The remaining credit needs are met from informal sources. Graph 2 Of all the loans taken by urban housholds, what percentage was formal and what percentage was informal? poor households well-off rich housholds with few assets households households BLUE Per cent of loans from the INFORMAL sector 85 15 PURPLE Per cent of loans from the FORMAL sector 10 90 72 28 53 47 2019-20

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108 Democratic Politics Thinking about political reforms Each of these challenges is linked to the possibility of reforms. As mentioned above, we discuss challenges only because we think these can be overcome. Generally all the suggestions or proposals about overcoming various challenges to democracy are called democracy reform or political reform. We are not going to give here a list of desirable political reforms, for there cannot be any such list. If all the countries do not have the same challenges, it follows that everyone cannot follow the same recipe of political reforms. We cannot prescribe a procedure for car repair without knowing which model the car is, what the defect is and what tools are available, where the car has broken down, etc. Can we at least have a list of such reforms for our country in todays context? We can develop some proposals for reforms at the national level. But the real challenge of reforms may not lie at the national level. Some of the crucial questions need to be thought at the State or local level. Besides, such a list may become irrelevant after some time. So, instead of that let us think of some broad guidelines that can be kept in mind while devising ways and means for political reforms in India l It is very tempting to think of legal ways of reforming politics, to think of new laws to ban undesirable things. But this temptation needs to be resisted. No doubt, law has an important role to play in political reform. Carefully devised changes in law can help to discourage wrong political practices and encourage good ones. But legal-constitutional changes by themselves cannot overcome challenges to democracy. This is like the rules of cricket. A change in rules for LBW decisions helped to reduce negative batting tactics. But no one would ever think that the quality of cricket could be improved mainly through changes in the rules. This is to be done mainly by the players, coaches and administrators. Similarly, democratic reforms are to be carried out mainly by political activists, parties, movements and politically conscious citizens. l Any legal change must carefully look at what results it will have on politics. Sometimes the results may be counter-productive. For example, many states have banned people who have more than two children from contesting panchayat elections. This has resulted in denial of democratic opportunity to many poor and women, which was not intended. Generally, laws that seek to ban something are not very successful in politics. Laws that give political actors incentives to do good things have more chances of working. The best laws are those which empower people to carry out democratic reforms. The Right to Information Act is a good example of a law that empowers the people to find out what is happening in government and act as watchdogs of democracy. Such a law helps to control corruption and supplements the existing laws that banned corruption and imposed strict penalties. l Democratic reforms are to be brought about principally through political practice. Therefore, the main focus of political reforms should be on ways to strengthen democratic practice. As we discussed in the chapter on political parties, the most important concern should be to increase and improve the quality of political participation by ordinary citizens. l Any proposal for political reforms should think not only about what is a good solution but also about who will implement it and how. It is not very wise to think that the legislatures will pass legislations that go against the interest of all the political parties and MPs. But measures that rely on democratic movements, citizens organisations and the media are likely to succeed. Let us keep these general guidelines in mind and look at some specific instances of challenges to democracy that require some measure of reform. Let us try to come up with some concrete proposals of reform. 2018-19

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India and the Contemporary World 102 Write in brief Project 1. Give two examples of different types of global exchanges which took place before the seventeenth century, choosing one example from Asia and one from the Americas. 2. Explain how the global transfer of disease in the pre-modern world helped in the colonisation of the Americas. 3. Write a note to explain the effects of the following a) The British governments decision to abolish the Corn Laws. b) The coming of rinderpest to Africa. c) The death of men of working-age in Europe because of the World War. d) The Great Depression on the Indian economy. e) The decision of MNCs to relocate production to Asian countries. 4. Give two examples from history to show the impact of technology on food availability. 5. What is meant by the Bretton Woods Agreement? Find out more about gold and diamond mining in South Africa in the nineteenth century. Who controlled the gold and diamond companies? Who were the miners and what were their lives like? Write in brief Discuss 6. Imagine that you are an indentured Indian labourer in the Caribbean. Drawing from the details in this chapter, write a letter to your family describing your life and feelings. 7. Explain the three types of movements or flows within international economic exchange. Find one example of each type of flow which involved India and Indians, and write a short account of it. 8. Explain the causes of the Great Depression. 9. Explain what is referred to as the G-77 countries. In what ways can G-77 be seen as a reaction to the activities of the Bretton Woods twins? Project Discuss 2018-19

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uestions 1. What are canal rays? 2. If an atom contains one electron and one proton, will it carry any charge or not? 4.2 The Structure of an Atom We have learnt Daltons atomic theory in Chapter 3, which suggested that the atom was indivisible and indestructible. But the discovery of two fundamental particles (electrons and protons) inside the atom, led to the failure of this aspect of Daltons atomic theory. It was then considered necessary to know how electrons and protons are arranged within an atom. For explaining this, many scientists proposed various atomic models. J.J. Thomson was the first one to propose a model for the structure of an atom. 4.2.1 THOMSONS MODEL OF AN ATOM Thomson proposed the model of an atom to be similar to that of a Christmas pudding. The electrons, in a sphere of positive charge, were like currants (dry fruits) in a spherical Christmas pudding. We can also think of a watermelon, the positive charge in the atom is spread all over like the red edible part of the watermelon, while the electrons are studded in the positively charged sphere, like the seeds in the watermelon (Fig. 4.1). Thomson proposed that (i) An atom consists of a positively charged sphere and the electrons are embedded in it. (ii) The negative and positive charges are equal in magnitude. So, the atom as a whole is electrically neutral. Although Thomsons model explained that atoms are electrically neutral, the results of experiments carried out by other scientists could not be explained by this model, as we will see below. 4.2.2 RUTHERFORDS MODEL OF AN ATOM Ernest Rutherford was interested in knowing how the electrons are arranged within an atom. Rutherford designed an experiment for this. In this experiment, fast moving alpha ()-particles were made to fall on a thin gold foil. He selected a gold foil because he wanted as thin a layer as possible. This gold foil was about 1000 atoms thick. -particles are doubly-charged helium ions. Since they have a mass of 4 u, the fast-moving -particles have a considerable amount of energy. It was expected that -particles would be deflected by the sub-atomic particles in the gold atoms. Since the -particles were much heavier than the protons, he did not expect to see large deflections. Q Fig.4.1 Thomsons model of an atom J.J. Thomson (1856- 1940), a British physicist, was born in Cheetham Hill, a suburb of Manchester, on 18 December 1856. He was awarded the Nobel prize in Physics in 1906 for his work on the discovery of electrons. He directed the Cavendish Laboratory at Cambridge for 35 years and seven of his research assistants subsequently won Nobel prizes. STRUCTURE OF THE ATOM 47 2019-2020

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TRIANGLES 147 But AC2 AB2 BC2 (Given) (2) So, AC PR From (1) and (2) (3) Now, in ABC and PQR, AB PQ (By construction) BC QR (By construction) AC PR Proved in (3) above So, ABC PQR (SSS congruence) Therefore, B Q (CPCT) But Q 90 (By construction) So, B 90 Note Also see Appendix 1 for another proof of this theorem. Let us now take some examples to illustrate the use of these theorems. Example 10 In Fig. 6.48, ACB 90 and CD AB. Prove that 2 2 BC BD AD AC Solution ACD ABC (Theorem 6.7) So, AC AB AD AC or, AC2 AB . AD (1) Similarly, BCD BAC (Theorem 6.7) So, BC BA BD BC or, BC2 BA . BD (2) Therefore, from (1) and (2), 2 2 BC AC BA BD BD AB AD AD Example 11 A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches a window 6 m above the ground. Find the length of the ladder. Fig. 6.48 2019-20

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90 MATHEMATICS formed between the horizontal and the line of sight. Plenty of other examples can be given where lines and angles are used. In the subsequent chapters of geometry, you will be using these properties of lines and angles to deduce more and more useful properties. Let us first revise the terms and definitions related to lines and angles learnt in earlier classes. 6.2 Basic Terms and Definitions Recall that a part (or portion) of a line with two end points is called a line-segment and a part of a line with one end point is called a ray. Note that the line segment AB is denoted by AB , and its length is denoted by AB. The ray AB is denoted by AB , and a line is denoted by AB . However, we will not use these symbols, and will denote the line segment AB, ray AB, length AB and line AB by the same symbol, AB. The meaning will be clear from the context. Sometimes small letters l, m, n, etc. will be used to denote lines. If three or more points lie on the same line, they are called collinear points otherwise they are called non-collinear points. Recall that an angle is formed when two rays originate from the same end point. The rays making an angle are called the arms of the angle and the end point is called the vertex of the angle. You have studied different types of angles, such as acute angle, right angle, obtuse angle, straight angle and reflex angle in earlier classes (see Fig. 6.1). (i) acute angle 0 x 90 (ii) right angle y 90 (iii) obtuse angle 90 z 180 (iv) straight angle s 180 (v) reflex angle 180 t 360 Fig. 6.1 Types of Angles 2019-2020

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India and the Contemporary World 42 5.1 Other Ways of Becoming Modern Japan and China Early Vietnamese nationalists had a close relationship with Japan and China. They provided models for those looking to change, a refuge for those who were escaping French police, and a location where a wider Asian network of revolutionaries could be established. In the first decade of the twentieth century a go east movement became popular. In 1907-08 some 300 Vietnamese students went to Japan to acquire modern education. For many of them the primary objective was to drive out the French from Vietnam, overthrow the puppet emperor and re-establish the Nguyen dynasty that had been deposed by the French. These nationalists looked for foreign arms and help. They appealed to the Japanese as fellow Asians. Japan had modernised itself and had resisted colonisation by the West. Besides, its victory over Russia in 1907 proved its military capabilities. Vietnamese students established a branch of the Restoration Society in Tokyo but after 1908, the Japanese Ministry of Interior clamped down on them. Many, including Phan Boi Chau, were deported and forced to seek exile in China and Thailand. Developments in China also inspired Vietnamese nationalists. In 1911, the long established monarchy in China was overthrown by a popular movement under Sun Yat-sen, and a Republic was set up. Inspired by these developments, Vietnamese students organised the Association for the Restoration of Vietnam (Viet-Nam Quan Phuc Hoi). Now the nature of the anti-French independence movement changed. The objective was no longer to set up a constitutional monarchy but a democratic republic. Soon, however, the anti-imperialist movement in Vietnam came under a new type of leadership. Fig. 9 Cartoon of Vietnamese nationalists chasing away imperialists. In all such nationalist representations of struggle the nationalists appear heroic, marching ahead, while the imperial forces flee. 2018-19

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SCIENCE 18 Q They cannot be separated from the mixture by the process of filtration. But, a special technique of separation known as centrifugation (perform activity 2.5), can be used to separate the colloidal particles. The components of a colloidal solution are the dispersed phase and the dispersion medium. The solute-like component or the dispersed particles in a colloid form the dispersed phase, and the component in which the dispersed phase is suspended is known as the dispersing medium. Colloids are classified according to the state (solid, liquid or gas) of the dispersing medium and the dispersed phase. A few common examples are given in Table 2.1. From this table you can see that they are very common everyday life. uestions 1. Differentiate between homogen- eous and heterogeneous mixtures with examples. 2. How are sol, solution and suspension different from each other? 3. To make a saturated solution, 36 g of sodium chloride is dissolved in 100 g of water at 293 K. Find its concentration at this temperature. Tyndall effect can be observed when sunlight passes through the canopy of a dense forest. In the forest, mist contains tiny droplets of water, which act as particles of colloid dispersed in air. Fig. 2.4 The Tyndall effect Properties of a colloid A colloid is a heterogeneous mixture. The size of particles of a colloid is too small to be individually seen by naked eyes. Colloids are big enough to scatter a beam of light passing through it and make its path visible. They do not settle down when left undisturbed, that is, a colloid is quite stable. Table 2.1 Common examples of colloids Dispersed Dispersing Type Example phase Medium Liquid Gas Aerosol Fog, clouds, mist Solid Gas Aerosol Smoke, automobile exhaust Gas Liquid Foam Shaving cream Liquid Liquid Emulsion Milk, face cream Solid Liquid Sol Milk of magnesia, mud Gas Solid Foam Foam, rubber, sponge, pumice Liquid Solid Gel Jelly, cheese, butter Solid Solid Solid Sol Coloured gemstone, milky glass 2019-2020

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xi Contents Foreword iii A Letter for You v How to Use this Book vii Unit I Chapter 1 Power-sharing 1 Chapter 2 Federalism 13 Unit II Chapter 3 Democracy and Diversity 29 Chapter 4 Gender, Religion and Caste 39 Unit III Chapter 5 Popular Struggles and Movements 57 Chapter 6 Political Parties 71 Unit IV Chapter 7 Outcomes of Democracy 89 Chapter 8 Challenges to Democracy 101 2018-19

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India and the Contemporary World 24 Box 3 Meanings of the symbols Attribute Significance Broken chains Being freed Breastplate with eagle Symbol of the German empire strength Crown of oak leaves Heroism Sword Readiness to fight Olive branch around the sword Willingness to make peace Black, red and gold tricolour Flag of the liberal-nationalists in 1848, banned by the Dukes of the German states Rays of the rising sun Beginning of a new era With the help of the chart in Box 3, identify the attributes of Veits Germania and interpret the symbolic meaning of the painting. In an earlier allegorical rendering of 1836, Veit had portrayed the Kaisers crown at the place where he has now located the broken chain. Explain the significance of this change. Activity Fig. 18 The fallen Germania, Julius Hbner, 1850. Describe what you see in Fig. 17. What historical events could Hbner be referring to in this allegorical vision of the nation? Activity 2018-19

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20 Economics consumption and processing of primary product and own account production of fixed assets. Education helps individual to make better use of the economic opportunities available before him. Education and skill are the major determinants of the earning of any individual in the market. A majority of women have meagre education and low skill formation. Women are paid low compared to men. Most women work where job security is not there. Various activities relating to legal protection is meagre. Employment in this sector is characterised by irregular and low income. In this sector there is an absence of basic facilities like maternity leave, childcare and other social security systems. However, women with high education and skill formation are paid at par with the men. Among the organised sector, teaching and medicine attract them the most. Some women have entered administrative and other services including job, that need high levels of scientific and technological competence. Ask your sister or your classmate what she would like to take up as a career? Quality of Population The quality of population depends upon the literacy rate, health of a person indicated by life expectancy and skill formation acquired by the people of the country. The quality of the poulation ultimately decides the growth rate of the country. Literate and healthy population are an asset. Education Sakals education in the initial years of his life bore him the fruits in the later years in terms of a good job and salary. We saw education was an important input for the growth of Sakal. It opened new horizon for him, provided new aspiration and developed values of life. Not only for Sakal, education contributes towards the growth of society also. It enhances the Due to historical and cultural reasons there is a division of labour between men and women in the family. Women generally look after domestic chores and men work in the fields. Sakals mother Sheela cooks food, cleans utensils, washes clothes, cleans the house and looks after her children. Sakals father Buta cultivates the field, sells the produce in the market and earns money for the family. Sheela is not paid for the services delivered for upbringing of the family. Buta earns money, which he spends on rearing his family. Women are not paid for their service delivered in the family. The household work done by women is not recognised in the National Income. Geeta, mother of Vilas, earned an income by selling fish. Thus women are paid for their work when they enter the labour market. Their earning like that of their male counterpart is determined on the basis of education and skill. Activity Visit a village or colony located near to your residential area and note down the various activities undertaken by the people of that village or colony. If this is not possible, ask your neighbour what is their profession? In which of the three sectors will you categorise their work? Say whether these activities are economic or non-economic activities Vilas sells fish in the village market. Vilas cooks food for his family. Sakal works in the private firm. Sakal looks after his younger brother and sister. 2019-2020

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Science Test the pH values of solutions given in Table 2.2. Record your observations. What is the nature of each substance on the basis of your observations? Figure 2.7 Figure 2.7 Figure 2.7 Figure 2.7 Figure 2.7 pH of some common substances shown on a pH paper (colours are only a rough guide) The strength of acids and bases depends on the number of H ions and OH ions produced, respectively. If we take hydrochloric acid and acetic acid of the same concentration, say one molar, then these produce different amounts of hydrogen ions. Acids that give rise to more H ions are said to be strong acids, and acids that give less H ions are said to be weak acids. Can you now say what weak and strong bases are? Are plants and animals pH sensitive? Our body works within the pH range of 7.0 to 7.8. Living organisms can survive only in a narrow range of pH change. When pH of rain water is less than 5.6, it is called acid rain. When acid rain flows into the rivers, it lowers the pH of the river water. The survival of aquatic life in such rivers becomes difficult. Table 2.2 S. Solution Colour of Approx- Nature of No. pH paper -imate substance pH value 1 Saliva (before meal) 2 Saliva (after meal) 3 Lemon juice 4 Colourless aerated drink 5 Carrot juice 6 Coffee 7 Tomato juice 8 Tap water 9 1M NaOH 10 1M HCl 2019-20

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CIRCLES 207 You might have seen a pulley fitted over a well which is used in taking out water from the well. Look at Fig. 10.2. Here the rope on both sides of the pulley, if considered as a ray, is like a tangent to the circle representing the pulley. Is there any position of the line with respect to the circle other than the types given above? You can see that there cannot be any other type of position of the line with respect to the circle. In this chapter, we will study about the existence of the tangents to a circle and also study some of their properties. 10.2 Tangent to a Circle In the previous section, you have seen that a tangent to a circle is a line that intersects the circle at only one point. To understand the existence of the tangent to a circle at a point, let us perform the following activities Activity 1 Take a circular wire and attach a straight wire AB at a point P of the circular wire so that it can rotate about the point P in a plane. Put the system on a table and gently rotate the wire AB about the point P to get different positions of the straight wire see Fig. 10.3(i). In various positions, the wire intersects the circular wire at P and at another point Q1 or Q2 or Q3, etc. In one position, you will see that it will intersect the circle at the point P only (see position AB of AB). This shows that a tangent exists at the point P of the circle. On rotating further, you can observe that in all other positions of AB, it will intersect the circle at P and at another point, say R1 or R2 or R3, etc. So, you can observe that there is only one tangent at a point of the circle. While doing activity above, you must have observed that as the position AB moves towards the position A B, the common point, say Q1, of the line AB and the circle gradually comes nearer and nearer to the common point P. Ultimately, it coincides with the point P in the position AB of AB. Again note, what happens if AB is rotated rightwards about P? The common point R3 gradually comes nearer and nearer to P and ultimately coincides with P. So, what we see is The tangent to a circle is a special case of the secant, when the two end points of its corresponding chord coincide. Fig. 10.3 (i) Fig. 10.2 The word tangent comes from the Latin word tangere, which means to touch and was introduced by the Danish mathematician Thomas Fineke in 1583. 2019-20

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Food Security in India 45 Lets Discuss Does Ahmad have a regular income from rickshaw-pulling? How does the yellow card help Ahmad Story of Ahmad Ahmad is a rickshaw puller in Bangalore. He has shifted from Jhumri Taliah along with his 3 brothers, 2 sisters and old parents. He stays in a jhuggi. The survival of all members of his family depends on his daily earnings from pulling rickshaw. However, he does not have a secured employment and his earnings fluctuate every day. During some days he gets enough earning for him to save some amount after buying all his day-to-day necessities. On other days, he barely earns enough to buy his daily necessities. However, fortunately, Ahmad has a yellow card, which is PDS Card for below poverty line people. With this card, Ahmad gets sufficient quantity of wheat, rice, sugar and kerosene oil for his daily use. He gets these essentials at half of the market price. He purchases his monthly stock during a particular day when the ration shop is opened for below poverty people. In this way, Ahmad is able to eke out his survival with less than sufficient earnings for his big family where he is the only earning member. Lets Discuss Why is agriculture a seasonal activity? Why is Ramu unemployed for about four months in a year? What does Ramu do when he is unemployed? Who are supplementing income in Ramus family? Why does Ramu face difficulty when he is unable to have work? When is Ramu food insecure? run his family even with small earnings from rickshaw-pulling? The social composition along with the inability to buy food also plays a role in food insecurity. The SCs, STs and some sections of the OBCs (lower castes among them) who have either poor land-base or very low land productivity are prone to food insecurity. The people affected by natural disasters, who have to migrate to other areas in search of work, are also among the most food insecure people. A high incidence of malnutrition prevails among women. This is a matter of serious concern as it puts even the unborn baby at the risk of malnutrition. A large proportion of pregnant and nursing mothers and children under the age of 5 years constitute an important segment of the food insecure population. According to the National Health and Family Survey (NHFS) 199899, the number of such women and children is approximately 11 crore. The food insecure people are disproportionately large in some regions of the country, such as economically backward states with high incidence of poverty, tribal and remote areas, regions more prone to natural disasters etc. In fact, the states of Uttar Pradesh (eastern and south-eastern parts), Bihar, Jharkhand, Orissa, West Bengal, Chattisgarh, parts of Madhya Pradesh and Maharasthra account for largest number of food insecure people in the country. Hunger is another aspect indicating food insecurity. Hunger is not just an expression of poverty, it brings about poverty. The attainment of food security therefore involves eliminating current hunger and reducing the risks of future hunger. Hunger has chronic and seasonal dimensions. Chronic hunger is a consequence of diets persistently inadequate in terms of quantity andor 2019-2020

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though industrial output or the production of goods went up by more than nine times during the period, employment in the industry went up by around three times. The same applies to the tertiary sector as well. While production in the service sector rose by 14 times, employment in the service sector rose around five times. As a result, more than half of the workers in the country are working in the primary sector, mainly in agriculture, producing only a quarter of the GDP. In contrast to this, the secondary and tertiary sectors produce four-fifths of the produce whereas they employ less than half the people. Does this mean that the workers in agriculture are not producing as much as they could? What it means is that there are more people in agriculture than is necessary. So, even if you move a few people out, production will not be affected. In other words, workers in the agricultural sector are underemployed. For instance, take the case of a small farmer, Laxmi, owning about two hectares of unirrigated land dependent only on rain and growing crops, like jowar and arhar. All five members of her family work in the plot throughout the year. Why? They have nowhere else to go for work. You will see that everyone is working, none remains idle, but in actual fact, their labour effort gets divided. Each one is doing some work but no one is fully employed. This is the situation of underemployment, where people are apparently working but all of them are made to work less than their potential. This kind of underemployment is hidden in contrast to someone who does not have a job and is clearly visible as unemployed. Hence, it is also called disguised unemployment. Now, supposing a landlord, Sukhram, comes and hires one or two members of the family to work on his land. Laxmis family is now able to earn some extra income through wages. Since you do not need five people to look after that small plot, two people moving out does not affect production on their farm. In the above example, two people may move to work in a factory. Once again the earnings of the family would increase and they would also continue to produce as much from their land. There are lakhs of farmers like Laxmi in India. This means that even if we remove a lot of people from agricultural sector and provide them with proper work elsewhere, agricultural production will not suffer. The incomes of the people who take up other work would increase the total family income. This underemployment can also happen in other sectors. For example there are thousands of casual workers in the service sector in urban areas who search for daily employment. They are employed as painters, plumbers, repair persons and others doing odd jobs. Many of them dont find work everyday. Similarly, we see other people of the service sector on the street pushing a cart or selling something where they may spend the whole day but earn very little. They are doing this work because they do not have better opportunities. 2019-20

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SCIENCE 4 1.3 States of Matter Observe different types of matter around you. What are its different states? We can see that matter around us exists in three different states solid, liquid and gas. These states of matter arise due to the variation in the characteristics of the particles of matter. Now, let us study about the properties of these three states of matter in detail. 1.3.1 THE SOLID STATE Activity 1.9 Collect the following articles a pen, a book, a needle and a piece of wooden stick. Sketch the shape of the above articles in your notebook by moving a pencil around them. Do all these have a definite shape, distinct boundaries and a fixed volume? What happens if they are hammered, pulled or dropped? Are these capable of diffusing into each other? Try compressing them by applying force. Are you able to compress them? All the above are examples of solids. We can observe that all these have a definite shape, distinct boundaries and fixed volumes, that is, have negligible compressibility. Solids have a tendency to maintain their shape when subjected to outside force. Solids may break under force but it is difficult to change their shape, so they are rigid. Consider the following (a) What about a rubber band, can it change its shape on stretching? Is it a solid? (b) What about sugar and salt? When kept in different jars these take the shape of the jar. Are they solid? (c) What about a sponge? It is a solid yet we are able to compress it. Why? All the above are solids as A rubber band changes shape under force and regains the same shape when the force is removed. If excessive force is applied, it breaks. The shape of each individual sugar or salt crystal remains fixed, whether we take it in our hand, put it in a plate or in a jar. A sponge has minute holes, in which air is trapped, when we press it, the air is expelled out and we are able to compress it. 1.3.2 THE LIQUID STATE Activity 1.10 Collect the following (a) water, cooking oil, milk, juice, a cold drink. (b) containers of different shapes. Put a 50 mL mark on these containers using a measuring cylinder from the laboratory. What will happen if these liquids are spilt on the floor? Measure 50 mL of any one liquid and transfer it into different containers one by one. Does the volume remain the same? Does the shape of the liquid remain the same ? When you pour the liquid from one container into another, does it flow easily? We observe that liquids have no fixed shape but have a fixed volume. They take up the shape of the container in which they are kept. Liquids flow and change shape, so they are not rigid but can be called fluid. Refer to activities 1.4 and 1.5 where we saw that solids and liquids can diffuse into liquids. The gases from the atmosphere diffuse and dissolve in water. These gases, especially oxygen and carbon dioxide, are essential for the survival of aquatic animals and plants. All living creatures need to breathe for survival. The aquatic animals can breathe under water due to the presence of dissolved oxygen in water. Thus, we may conclude that solids, liquids and gases can diffuse into liquids. The rate of diffusion of liquids is 2019-2020

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Foreword iii History and a Changing World v Section I Events and Processes 1-74 I. The French Revolution 3 II. Socialism in Europe and the Russian Revolution 25 III. Nazism and the Rise of Hitler 49 Section II Livelihoods, Economies and Societies 75-116 IV. Forest Society and Colonialism 77 V. Pastoralists in the Modern World 97 CREDITS 117 Contents 2019-2020

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Metals and Non-metals You may have observed the following general properties for ionic compounds (i) Physical nature Ionic compounds are solids and are somewhat hard because of the strong force of attraction between the positive and negative ions. These compounds are generally brittle and break into pieces when pressure is applied. (ii) Melting and Boiling points Ionic compounds have high melting and boiling points (see Table 3.4). This is because a considerable amount of energy is required to break the strong inter-ionic attraction. (iii) Solubility Electrovalent compounds are generally soluble in water and insoluble in solvents such as kerosene, petrol, etc. (iv) Conduction of Electricity The conduction of electricity through a solution involves the movement of charged particles. A solution of an ionic compound in water contains ions, which move to the opposite electrodes when electricity is passed through the solution. Ionic compounds in the solid state do not conduct electricity because movement of ions in the solid is not possible due to their rigid structure. But ionic compounds conduct electricity in the molten state. This is possible in the molten state since the elecrostatic forces of attraction between the oppositely charged ions are overcome due to the heat. Thus, the ions move freely and conduct electricity. 1. (i) Write the electron-dot structures for sodium, oxygen and magnesium. (ii) Show the formation of Na2O and MgO by the transfer of electrons. (iii) What are the ions present in these compounds? 2. Why do ionic compounds have high melting points? The earths crust is the major source of metals. Seawater also contains some soluble salts such as sodium chloride, magnesium chloride, etc. The elements or compounds, which occur naturally in the earths crust, are known as minerals. At some places, minerals contain a very high percentage of a particular metal and the metal can be profitably extracted from it. These minerals are called ores. You have learnt about the reactivity series of metals. Having this knowledge, you can easily understand how a metal is extracted from its ore. Some metals are found in the earths crust in the free state. Some are found in the form of their compounds. The metals at the bottom of the activity series are the least reactive. They are often found in a free 2019-20

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Light Reflection and Refraction Figure 10.16 Figure 10.16 Figure 10.16 Figure 10.16 Figure 10.16 The position, size and the nature of the image formed by a convex lens for various positions of the object Figure 10.17 Figure 10.17 Figure 10.17 Figure 10.17 Figure 10.17 Nature, position and relative size of the image formed by a concave lens For lenses, we follow sign convention, similar to the one used for spherical mirrors. We apply the rules for signs of distances, except that all measurements are taken from the optical centre of the lens. According to the convention, the focal length of a convex lens is positive and that of a concave lens is negative. You must take care to apply appropriate signs for the values of u, v, f, object height h and image height h. As we have a formula for spherical mirrors, we also have formula for spherical lenses. This formula gives the relationship between object- distance (u), image-distance (v) and the focal length (f ). The lens formula is expressed as 1 1 1 v u f (10.8) The lens formula given above is general and is valid in all situations for any spherical lens. Take proper care of the signs of different quantities, while putting numerical values for solving problems relating to lenses. 2019-20

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PAIR OF LINEAR EQUATIONS IN TWO VARIABLES 57 2. Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method (i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1 2 if we only add 1 to the denominator. What is the fraction? (ii) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu? (iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number. (iv) Meena went to a bank to withdraw 2000. She asked the cashier to give her 50 and 100 notes only. Meena got 25 notes in all. Find how many notes of 50 and 100 she received. (v) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid 27 for a book kept for seven days, while Susy paid 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day. 3.4.3 Cross - Multiplication Method So far, you have learnt how to solve a pair of linear equations in two variables by graphical, substitution and elimination methods. Here, we introduce one more algebraic method to solve a pair of linear equations which for many reasons is a very useful method of solving these equations. Before we proceed further, let us consider the following situation. The cost of 5 oranges and 3 apples is 35 and the cost of 2 oranges and 4 apples is 28. Let us find the cost of an orange and an apple. Let us denote the cost of an orange by x and the cost of an apple by y. Then, the equations formed are 5x 3y 35, i.e., 5x 3y 35 0 (1) 2x 4y 28, i.e., 2x 4y 28 0 (2) Let us use the elimination method to solve these equations. Multiply Equation (1) by 4 and Equation (2) by 3. We get (4)(5)x (4)(3)y (4)(35) 0 (3) (3)(2)x (3)(4)y (3)(28) 0 (4) Subtracting Equation (4) from Equation (3), we get (5)(4) (3)(2)x (4)(3) (3)(4)y 4(35) (3)(28) 0 2019-20

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TRIANGLES 113 See that these two triangles are not congruent. Repeat this activity with some more pairs of triangles. So, equality of one pair of sides or one pair of sides and one pair of angles is not sufficient to give us congruent triangles. What would happen if the other pair of arms (sides) of the equal angles are also equal? In Fig 7.7, BC QR, B Q and also, AB PQ. Now, what can you say about congruence of ABC and PQR? Recall from your earlier classes that, in this case, the two triangles are congruent. Verify this for ABC and PQR in Fig. 7.7. Repeat this activity with other pairs of triangles. Do you observe that the equality of two sides and the included angle is enough for the congruence of triangles? Yes, it is enough. Fig. 7.7 This is the first criterion for congruence of triangles. Axiom 7.1 (SAS congruence rule) Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle. This result cannot be proved with the help of previously known results and so it is accepted true as an axiom (see Appendix 1). Let us now take some examples. Example 1 In Fig. 7.8, OA OB and OD OC. Show that (i) AOD BOC and (ii) AD BC. Solution (i) You may observe that in AOD and BOC, OA OB (Given) OD OC Fig. 7.8 2019-2020

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72 DEMOCRATIC POLITICS 4 Which of the following institutions can make changes to an existing law of the country? a The Supreme Court b The President c The Prime Minister d The Parliament 5 Match the ministry with the news that the ministry may have released exercises a A new policy is being made to increase the jute exports from the country. b Telephone services will be made more accessible to rural areas. c The price of rice and wheat sold under the Public Distribution System will go down. d A pulse polio campaign will be launched. e The allowances of the soldiers posted on high altitudes will be increased. i Ministry of Defence ii Ministry of Agriculture, Food and Public Distribution iii Ministry of Health iv Ministry of Commerce and Industry v Ministry of Communications and Information Technology 6 Of all the institutions that we have studied in this chapter, name the one that exercises the powers on each of the following matters. a Decision on allocation of money for developing infrastructure like roads, irrigation etc. and different welfare activities for the citizens b Considers the recommendation of a Committee on a law to regulate the stock exchange c Decides on a legal dispute between two state governments d Implements the decision to provide relief for the victims of an earthquake. 7 Why is the Prime Minister in India not directly elected by the people? Choose the most appropriate answer and give reasons for your choice. a In a Parliamentary democracy only the leader of the majority party in the Lok Sabha can become the Prime Minister. b Lok Sabha can remove the Prime Minister and the Council of Ministers even before the expiry of their term. c Since the Prime Minister is appointed by the President there is no need for it. d Direct election of the Prime Minister will involve lot of expenditure on election. 8 Three friends went to watch a film that showed the hero becoming Chief Minister for a day and making big changes in the state. Imran said this is what the country needs. Rizwan said this kind of a personal 2019-20

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Until the middle of the twentieth century, production was largely organised within countries. What crossed the boundaries of these countries were raw material, food stuff and finished products. Colonies such as India exported raw materials and food stuff and imported finished goods. Trade was the main channel connecting distant countries. This was before large companies called A large MNC, producing industrial equipment, designs its products in research centres in the United States, and then has the components manufactured in China. These are then shipped to Mexico and Eastern Europe where the products are assembled and the finished products are sold all over the world. Meanwhile, the companys customer care is carried out through call centres located in India. multinational corporations (MNCs) emerged on the scene. A MNC is a company that owns or controls production in more than one nation. MNCs set up offices and factories for production in regions where they can get cheap labour and other resources. This is done so that the cost of production is low and the MNCs can earn greater profits. Consider the following example. This is a call centre in Bengaluru, equipped with telecom facilities and access to the Internet to provide information and support to customers abroad. 2019-20

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SCIENCE 166 pleasant is said to be of a rich quality. A sound of single frequency is called a tone. The sound which is produced due to a mixture of several frequencies is called a note and is pleasant to listen to. Noise is unpleasant to the ear! Music is pleasant to hear and is of rich quality. uestions 1. Which wave property determines (a) loudness, (b) pitch? 2. Guess which sound has a higher pitch guitar or car horn? The speed of sound is defined as the distance which a point on a wave, such as a compression or a rarefaction, travels per unit time. We know, speed, v distance time T Here is the wavelength of the sound wave. It is the distance travelled by the sound wave in one time period (T) of the wave. Thus, v or v That is, speed wavelength frequency. The speed of sound remains almost the same for all frequencies in a given medium under the same physical conditions. Example 12.1 A sound wave has a frequency of 2 kHz and wave length 35 cm. How long will it take to travel 1.5 km? Solution Given, Frequency, 2 kHz 2000 Hz Wavelength, 35 cm 0.35 m We know that speed, v of the wave wavelength frequency v 0.35 m 2000 Hz 700 ms The time taken by the wave to travel a distance, d of 1.5 km is Thus sound will take 2.1 s to travel a distance of 1.5 km. uestions 1. What are wavelength, frequency, time period and amplitude of a sound wave? 2. How are the wavelength and frequency of a sound wave related to its speed? 3. Calculate the wavelength of a sound wave whose frequency is 220 Hz and speed is 440 ms in a given medium. 4. A person is listening to a tone of 500 Hz sitting at a distance of 450 m from the source of the sound. What is the time interval between successive compressions from the source? The amount of sound energy passing each second through unit area is called the intensity of sound. We sometimes use the terms loudness and intensity interchangeably, but they are not the same. Loudness is a measure of the response of the ear to the sound. Even when two sounds are of equal intensity, we may hear one as louder than the other simply because our ear detects it better. uestion 1. Distinguish between loudness and intensity of sound. 12.2.4 SPEED OF SOUND IN DIFFERENT MEDIA Sound propagates through a medium at a finite speed. The sound of a thunder is heard a little later than the flash of light is seen. Q Q Q 2019-2020

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SCIENCE 200 14.4.4 THE OXYGEN-CYCLE Oxygen is a very abundant element on our Earth. It is found in the elemental form in the atmosphere to the extent of 21. It also occurs extensively in the combined form in the Earths crust as well as also in the air in the form of carbon dioxide. In the crust, it is found as the oxides of most metals and silicon, and also as carbonate, sulphate, nitrate and other minerals. It is also an essential component of most biological molecules like carbohydrates, proteins, nucleic acids and fats (or lipids). But when we talk of the oxygen-cycle, we are mainly referring to the cycle that maintains the levels of oxygen in the atmosphere. Oxygen from the atmosphere is used up in three processes, namely combustion, respiration and in the formation of oxides of nitrogen. Oxygen is returned to the atmosphere in only one major process, that is, photosynthesis. And this forms the broad outline of the oxygen-cycle in nature (Fig. 14.8). bacteria, are poisoned by elemental oxygen. In fact, even the process of nitrogen-fixing by bacteria does not take place in the presence of oxygen. 14.5 Ozone Layer Elemental oxygen is normally found in the form of a diatomic molecule. However, in the upper reaches of the atmosphere, a molecule containing three atoms of oxygen is found. This would mean a formula of O3 and this is called ozone. Unlike the normal diatomic molecule of oxygen, ozone is poisonous and we are lucky that it is not stable nearer to the Earths surface. But it performs an essential function where it is found. It absorbs harmful radiations from the Sun. This prevents those harmful radiations from reaching the surface of the Earth where they may damage many forms of life. Recently it was discovered that this ozone layer was getting depleted. Various man-made compounds like CFCs (carbon compounds having both fluorine and chlorine which are very stable and not degraded by any biological process) were found to persist in the atmosphere. Once they reached the ozone layer, they would react with the ozone molecules. This resulted in a reduction of the ozone layer and recently they have discovered a hole in the ozone layer above the Antartica. It is difficult to imagine the consequences for life on Earth if the ozone layer dwindles further, but many people think that it would be better not to take chances. These people advocate working towards stopping all further damage to the ozone layer. Fig. 14.8 Oxygen-cycle in nature Though we usually think of oxygen as being necessary to life in the process of respiration, it might be of interest to you to learn that some forms of life, especially Fig. 14.9 Satellite picture showing the hole (magenta colour) in the ozone layer over Antartica October 1980 October 1985 October 1990 2019-2020

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326 MATHEMATICS EXERCISE 1.3 1. (i) 0.36, terminating. (ii) 0.09 , non-terminating repeating. (iii) 4.125, terminating. (iv) 0.230769 , non-terminating repeating. (v) 0.18 non-terminating repeating. (vi) 0.8225 terminating. 2. 2 1 2 0.285714, 7 7 3 1 3 0.428571, 7 7 4 1 4 0.571428, 7 7 5 1 5 0.714285, 7 7 6 1 6 0.857142 7 7 3. (i) 2 3 Let x 0.666. . . So 10x 6.666. . . or, 10x 6 x or , x 6 2 9 3 (ii) 43 90 (iii) 1 999 4. 1 Let x 0.9999. . . So 10 x 9.999. . . or, 10 x 9 x or, x 1 5. 0.0588235294117647 6. The prime factorisation of q has only powers of 2 or powers of 5 or both. 7. 0.01001000100001. . ., 0.202002000200002. . ., 0.003000300003. . . 8. 0.75075007500075000075. . ., 0.767076700767000767. . ., 0.808008000800008. . . 9. (i) and (v) irrational (ii), (iii) and (iv) rational. EXERCISE 1.4 1. Proceed as in Section 1.4 for 2.665. 2. Proceed as in Example 11. EXERCISE 1.5 1. (i) Irrational (ii) Rational (iii) Rational (iv) Irrational (v) Irrational 2. (i) 6 3 2 2 3 6 (ii) 6 (iii) 7 2 10 (iv) 3 3. There is no contradiction. Remember that when you measure a length with a scale or any other device, you only get an approximate rational value. So, you may not realise that either c or d is irrational. 2019-2020

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Sustainable Management of Natural Resources Lastly, we come to the nature and wildlife enthusiasts who are in no way dependent on the forests, but who may have considerable say in their management. The conservationists were initially taken up with large animals like lions, tigers, elephants and rhinoceros. They now recognise the need to preserve biodiversity as a whole. But shouldnt we recognise people as forming part of the forest system? There have been enough instances of local people working traditionally for conservation of forests. For example, the case of Bishnois community living in western Rajasthan on the border of the Thar desert. Conservation of forest and wildlife has been a religious tenet for them. These nature-loving people have for centuries, been conserving the flora and fauna to the extent of sacrificing their lives to protect the environment. They are living with the basic philosophy that all living things have a right to survive and share all resources. The Government of India has recently instituted an Amrita Devi Bishnoi National Award for Wildlife Conservation in the memory of Amrita Devi Bishnoi, who in 1731 sacrificed her life along with 363 others for the protection of khejri trees in Khejrali village near Jodhpur in Rajasthan. Studies have shown that the prejudice against the traditional use of forest areas has no basis. Here is an example the great Himalayan National Park contains, within its reserved area, alpine meadows which were grazed by sheep in summer. Nomadic shepherds drove their flock up from the valleys every summer. When this national park was formed, this practice was put to an end. Now it is seen that without the regular grazing by sheep the grass first grows very tall, and then falls over preventing fresh growth. Management of protected areas by keeping the local people out or by using force cannot possibly be successful in the long run. In any case, the damage caused to forests cannot be attributed to only the local people one cannot turn a blind eye to the deforestation caused by industrial needs or development projects like building roads or dams. The damage caused in these reserves by tourists or the arrangements made for their convenience is also to be considered. We need to accept that human intervention has been very much a part of the forest landscape. What has to be managed in the nature and what may be the extent of this intervention? Forest resources ought to be used in a manner that is both environmentally and developmentally sound in other words, while the environment is preserved, the benefits of the controlled exploitation go to the local people, a process in which decentralised economic growth and ecological conservation go hand in hand. The kind of economic and social development we want will ultimately determine whether the environment will be conserved or further destroyed. The environment must not be regarded as a pristine collection of plants and animals. It is a vast and complex entity that offers a range of natural resources for our use. We need to use these resources with due caution for our economic and social growth, and to meet our material aspirations. Figure 16.3 Figure 16.3 Figure 16.3 Figure 16.3 Figure 16.3 Khejri Tree 2019-20

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18 MATHEMATICS 2. Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions. 3. The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form , p q what can you say about the prime factors of q? (i) 43.123456789 (ii) 0.120120012000120000. . . (iii) 43.123456789 1.6 Summary In this chapter, you have studied the following points 1. Euclids division lemma Given positive integers a and b, there exist whole numbers q and r satisfying a bq r, 0 r b. 2. Euclids division algorithm This is based on Euclids division lemma. According to this, the HCF of any two positive integers a and b, with a b, is obtained as follows Step 1 Apply the division lemma to find q and r where a bq r, 0 r b. Step 2 If r 0, the HCF is b. If r 0, apply Euclids lemma to b and r. Step 3 Continue the process till the remainder is zero. The divisor at this stage will be HCF (a, b). Also, HCF(a, b) HCF(b, r). 3. The Fundamental Theorem of Arithmetic Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur. 4. If p is a prime and p divides a2, then p divides a, where a is a positive integer. 5. To prove that 2, 3 are irrationals. 6. Let x be a rational number whose decimal expansion terminates. Then we can express x in the form p q , where p and q are coprime, and the prime factorisation of q is of the form 2n5m, where n, m are non-negative integers. 7. Let x p q be a rational number, such that the prime factorisation of q is of the form 2n5m, where n, m are non-negative integers. Then x has a decimal expansion which terminates. 8. Let x p q be a rational number, such that the prime factorisation of q is not of the form 2n 5m, where n, m are non-negative integers. Then x has a decimal expansion which is non-terminating repeating (recurring). 2019-20

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234 MATHEMATICS Example 6 Find the area of the shaded design in Fig. 12.17, where ABCD is a square of side 10 cm and semicircles are drawn with each side of the square as diameter. (Use 3.14) Fig. 12.17 Fig. 12.18 Solution Let us mark the four unshaded regions as I, II, III and IV (see Fig. 12.18). Area of I Area of III Area of ABCD Areas of two semicircles of each of radius 5 cm 2 2 1 10 10 2 5 cm 2 (100 3.14 25) cm2 (100 78.5) cm2 21.5 cm2 Similarly, Area of II Area of IV 21.5 cm2 So, area of the shaded design Area of ABCD Area of (I II III IV) (100 2 21.5) cm2 (100 43) cm2 57 cm2 EXERCISE 12.3 Unless stated otherwise, use 22 7 1. Find the area of the shaded region in Fig. 12.19, if PQ 24 cm, PR 7 cm and O is the centre of the circle. Fig. 12.19 2019-20

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NUMBER SYSTEMS 5 EXERCISE 1.1 1. Is zero a rational number? Can you write it in the form p q , where p and q are integers and q 0? 2. Find six rational numbers between 3 and 4. 3. Find five rational numbers between 3 5 and 4 5 . 4. State whether the following statements are true or false. Give reasons for your answers. (i) Every natural number is a whole number. (ii) Every integer is a whole number. (iii) Every rational number is a whole number. 1.2 Irrational Numbers We saw, in the previous section, that there may be numbers on the number line that are not rationals. In this section, we are going to investigate these numbers. So far, all the numbers you have come across, are of the form p q , where p and q are integers and q 0. So, you may ask are there numbers which are not of this form? There are indeed such numbers. The Pythagoreans in Greece, followers of the famous mathematician and philosopher Pythagoras, were the first to discover the numbers which were not rationals, around 400 BC. These numbers are called irrational numbers (irrationals), because they cannot be written in the form of a ratio of integers. There are many myths surrounding the discovery of irrational numbers by the Pythagorean, Hippacus of Croton. In all the myths, Hippacus has an unfortunate end, either for discovering that 2 is irrational or for disclosing the secret about 2 to people outside the secret Pythagorean sect! Let us formally define these numbers. A number s is called irrational, if it cannot be written in the form p q , where p and q are integers and q 0. Pythagoras (569 BCE 479 BCE) Fig. 1.3 2019-2020

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ATOMS AND MOLECULES 41 molecules, ions or particles) is that quantity in number having a mass equal to its atomic or molecular mass in grams. The number of particles (atoms, molecules or ions) present in 1 mole of any substance is fixed, with a value of 6.022 1023. This is an experimentally obtained value. This number is called the Avogadro Constant or Avogadro Number (represented by N0), named in honour of the Italian scientist, Amedeo Avogadro. 1 mole (of anything) 6.022 1023 in number, as, 1 dozen 12 nos. 1 gross 144 nos. Besides being related to a number, a mole has one more advantage over a dozen or a gross. This advantage is that mass of 1 mole of a particular substance is also fixed. The mass of 1 mole of a substance is equal to its relative atomic or molecular mass in grams. The atomic mass of an element gives us the mass of one atom of that element in atomic mass units (u). To get the mass of 1 mole of atom of that element, that is, molar mass, we have to take the same numerical value but change the units from u to g. Molar mass of atoms is also known as gram atomic mass. For example, atomic mass of hydrogen1u. So, gram atomic mass of hydrogen 1 g. 1 u hydrogen has only 1 atom of hydrogen 1 g hydrogen has 1 mole atoms, that is, 6.022 1023 atoms of hydrogen. Similarly, 16 u oxygen has only 1 atom of oxygen, 16 g oxygen has 1 mole atoms, that is, 6.022 1023 atoms of oxygen. To find the gram molecular mass or molar mass of a molecule, we keep the numerical value the same as the molecular mass, but simply change units as above from u to g. For example, as we have already calculated, molecular mass of water (H2O) is 18 u. From here we understand that 18 u water has only 1 molecule of water, 18 g water has 1 mole molecules of water, that is, 6.022 1023 molecules of water. Chemists need the number of atoms and molecules while carrying out reactions, and for this they need to relate the mass in grams to the number. It is done as follows 1 mole 6.022 1023 number Relative mass in grams. Thus, a mole is the chemists counting unit. The word mole was introduced around 1896 by Wilhelm Ostwald who derived the term from the Latin word moles meaning a heap or pile. A substance may be considered as a heap of atoms or molecules. The unit mole was accepted in 1967 to provide a simple way of reporting a large number the massive heap of atoms and molecules in a sample. Example 3.3 1. Calculate the number of moles for the following (i) 52 g of He (finding mole from mass) (ii) 12.044 1023 number of He atoms (finding mole from number of particles). Solutions No. of moles n Given mass m Molar mass M Given number of particles N Avogadro number of particles N0 (i) Atomic mass of He 4 u Molar mass of He 4g Thus, the number of moles given mass molar mass n m M 52 4 13 (ii) we know, 1 mole 6.022 1023 The number of moles given number of particles Avogadro number n N No 12 044 10 6 022 10 2 23 23 . . 2019-2020

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India and the Contemporary World 112 The loss of the finest grazing lands and water resources created pressure on the small area of land that the Maasai were confined within. Continuous grazing within a small area inevitably meant a deterioration of the quality of pastures. Fodder was always in short supply. Feeding the cattle became a persistent problem. 3.2 The Borders are Closed In the nineteenth century, African pastoralists could move over vast areas in search of pastures. When the pastures were exhausted in one place they moved to a different area to graze their cattle. From the late nineteenth century, the colonial government began imposing various restrictions on their mobility. Like the Maasai, other pastoral groups were also forced to live within the confines of special reserves. The boundaries of these reserves became the limits within which they could now move. They were not allowed to move out with their stock without special permits. And it was difficult to get permits without trouble and harassment. Those found guilty of disobeying the rules were severely punished. Pastoralists were also not allowed to enter the markets in white areas. In many regions, they were prohibited from participating in any form of trade. White settlers and European colonists saw pastoralists as dangerous and savage people with whom all contact had to be minimised. Cutting off all links was, however, never really possible, because white colonists had to depend on black labour to bore mines and, build roads and towns. The new territorial boundaries and restrictions imposed on them suddenly changed the lives of pastoralists. This adversely affected Source F In most places in colonial Africa, the police were given instructions to keep a watch on the movements of pastoralists, and prevent them from entering white areas. The following is one such instruction given by a magistrate to the police, in south-west Africa, restricting the movements of the pastoralists of Kaokoland in Namibia Passes to enter the Territory should not be given to these Natives unless exceptional circumstances necessitate their entering The object of the above proclamation is to restrict the number of natives entering the Territory and to keep a check on them, and ordinary visiting passes should therefore never be issued to them. Kaokoveld permits to enter, Magistrate to Police Station Commanders of Outjo and Kamanjab, 24 November, 1937. Source 2019-2020

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SURFACE AREAS AND VOLUMES 251 Solution Radius of the hemispherical tank 3 2 m Volume of the tank 3 3 2 22 3 m 3 7 2 3 99 m 14 So, the volume of the water to be emptied 3 1 99 m 2 14 99 1000 28 litres 99000 28 litres Since, 25 7 litres of water is emptied in 1 second, 99000 28 litres of water will be emptied in 99000 7 28 25 seconds, i.e., in 16.5 minutes. EXERCISE 13.3 Take 22 7 , unless stated otherwise. 1. A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder. 2. Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere. 3. A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform. 4. A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment. 5. A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream. 6. How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm 10 cm 3.5 cm? 2019-20

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SCIENCE 170 five and some animals, such as dogs can hear up to 25 kHz (1 kHz 1000 Hz). As people grow older their ears become less sensitive to higher frequencies. Sounds of frequencies below 20 Hz are called infrasonic sound or infrasound. If we could hear infrasound we would hear the vibrations of a pendulum just as we hear the vibrations of the wings of a bee. Rhinoceroses communicate using infrasound of frequency as low as 5 Hz. Whales and elephants produce sound in the infrasound range. It is observed that some animals get disturbed before earthquakes. Earthquakes produce low-frequency infrasound before the main shock waves begin which possibly alert the animals. Frequencies higher than 20 kHz are called ultrasonic sound or ultrasound. Ultrasound is produced by animals such as dolphins, bats and porpoises. Moths of certain families have very sensitive hearing equipment. These moths can hear the high frequency squeaks of the bat and know when a bat is flying nearby, and are able to escape capture. Rats also play games by producing ultrasound. Hearing Aid People with hearing loss may need a hearing aid. A hearing aid is an electronic, battery operated device. The hearing aid receives sound through a microphone. The microphone converts the sound waves to electrical signals. These electrical signals are amplified by an amplifier. The amplified electrical signals are given to a speaker of the hearing aid. The speaker converts the amplified electrical signal to sound and sends to the ear for clear hearing. uestions 1. What is the audible range of the average human ear? 2. What is the range of frequencies associated with (a) Infrasound? (b) Ultrasound? 12.5 Applications of Ultrasound Ultrasounds are high frequency waves. Ultrasounds are able to travel along well- defined paths even in the presence of obstacles. Ultrasounds are used extensively in industries and for medical purposes. Ultrasound is generally used to clean parts located in hard-to-reach places, for example, spiral tube, odd shaped parts, electronic components etc. Objects to be cleaned are placed in a cleaning solution and ultrasonic waves are sent into the solution. Due to the high frequency, the particles of dust, grease and dirt get detached and drop out. The objects thus get thoroughly cleaned. Ultrasounds can be used to detect cracks and flaws in metal blocks. Metallic components are generally used in construction of big structures like buildings, bridges, machines and also scientific equipment. The cracks or holes inside the metal blocks, which are invisible from outside reduces the strength of the structure. Ultrasonic waves are allowed to pass through the metal block and detectors are used to detect the transmitted waves. If there is even a small defect, the ultrasound gets reflected back indicating the presence of the flaw or defect, as shown in Fig. 12.16. Q Fig 12.16 Ultrasound is reflected back from the defective locations inside a metal block. 2019-2020

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16 Economics Overview The chapter People as Resource is an effort to explain population as an asset for the economy rather than a liability. Population becomes human capital when there is investment made in the form of education, training and medical care. In fact, human capital is the stock of skill and productive knowledge embodied in them. People as Resource is a way of referring to a countrys working people in terms of their existing productive skills and abilities. Looking at the population from this productive aspect emphasises its ability to contribute to the creation of the Gross National Product. Like other resources population also is a resource a human resource. This is the positive side of a large population that is often overlooked when we look only at the negative side, considering only the problems of providing the population with food, education and access to health facilities. When the existing human resource is further developed by becoming more educated and healthy, we call it human capital formation that adds to the productive power of the country just like physical capital formation. Investment in human capital (through education, training, medical care) yields a return just like investment in physical capital. This can be seen directly in the form of higher incomes earned because of higher productivity of the more educated or the better trained persons, as well as the higher productivity of healthier people. People as Resource 2 Chapter Indias Green Revolution is a dramatic example of how the input of greater knowledge in the form of improved production technologies can rapidly increase the productivity of scarce land resources. Indias IT revolution is a striking instance of how the importance of human capital has come to acquire a higher position than that of material, plant and machinery. Source Planning Commission, Govt. of India. People as Resource 2 2019-2020

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Chemical Reactions and Equations Why does the iron nail become brownish in colour and the blue colour of copper sulphate solution fades? The following chemical reaction takes place in this Activity Fe(s) CuSO4(aq) FeSO4(aq) Cu(s) (1.24) (Copper sulphate) (Iron sulphate) In this reaction, iron has displaced or removed another element, copper, from copper sulphate solution. This reaction is known as displacement reaction. Other examples of displacement reactions are Zn(s) CuSO4(aq) ZnSO4(aq) Cu(s) (1.25) (Copper sulphate) (Zinc sulphate) Pb(s) CuCl2(aq) PbCl2(aq) Cu(s) (1.26) (Copper chloride) (Lead chloride) Zinc and lead are more reactive elements than copper. They displace copper from its compounds. Take about 3 mL of sodium sulphate solution in a test tube. In another test tube, take about 3 mL of barium chloride solution. Mix the two solutions (Fig. 1.9). What do you observe? Figure 1.9 Figure 1.9 Figure 1.9 Figure 1.9 Figure 1.9 Formation of barium sulphate and sodium chloride You will observe that a white substance, which is insoluble in water, is formed. This insoluble substance formed is known as a precipitate. Any reaction that produces a precipitate can be called a precipitation reaction. Na2SO4(aq) BaCl2(aq) BaSO4(s) 2NaCl(aq) (1.27) (Sodium (Barium (Barium (Sodium sulphate) chloride) sulphate) chloride) Figure 1.8 Figure 1.8 Figure 1.8 Figure 1.8 Figure 1.8 (b) Iron nails and copper sulphate solutions compared before and after the experiment 2019-20

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STATISTICS 285 Solution Class intervals Frequency Cumulative frequency 0 - 100 2 2 100 - 200 5 7 200 - 300 x 7 x 300 - 400 12 19 x 400 - 500 17 36 x 500 - 600 20 56 x 600 - 700 y 56 x y 700 - 800 9 65 x y 800 - 900 7 72 x y 900 - 1000 4 76 x y It is given that n 100 So, 76 x y 100, i.e., x y 24 (1) The median is 525, which lies in the class 500 600 So, l 500, f 20, cf 36 x, h 100 Using the formula Median cf 2 , n l h f we get 525 50 36 500 100 20 x i.e., 525 500 (14 x) 5 i.e., 25 70 5x i.e., 5x 70 25 45 So, x 9 Therefore, from (1), we get 9 y 24 i.e., y 15 2019-20

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NATURAL RESOURCES 199 adds to the carbon dioxide in the atmosphere is the process of combustion where fuels are burnt to provide energy for various needs like heating, cooking, transportation and industrial processes. In fact, the percentage of carbon dioxide in the atmosphere is said to have doubled since the industrial revolution when human beings started burning fossil fuels on a very large scale. Carbon, like water, is thus cycled repeatedly through different forms by the various physical and biological activities. 14.4.3 (i) THE GREENHOUSE EFFECT Recall the reading taken by you under (iii) in Activity 14.1. Heat is trapped by glass, and hence the temperature inside a glass enclosure will be much higher than the surroundings. This phenomenon was used to create an enclosure where tropical plants Fig. 14.7 Carbon-cycle in nature could be kept warm during the winters in colder climates. Such enclosures are called greenhouses. Greenhouses have also lent their name to an atmospheric phenomenon. Some gases prevent the escape of heat from the Earth. An increase in the percentage of such gases in the atmosphere would cause the average temperatures to increase world-wide and this is called the greenhouse effect. Carbon dioxide is one of the greenhouse gases. An increase in the carbon dioxide content in the atmosphere would cause more heat to be retained by the atmosphere and lead to global warming. Activity 14.12 Find out what the consequences of global warming would be. Also, find out the names of some other greenhouse gases. 2019-2020

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