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. 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	[ 3540, 56682, 220, 21, 17, 14804, 1052, 264, 6319, 398, 57819, 11, 64151, 476, 60037, 11, 12756, 12681, 5944, 3143, 279, 12261, 315, 1817, 2779, 30, 1096, 5944, 374, 2598, 61507, 13, 38970, 1052, 4428, 14389, 304, 37327, 57112, 7761, 30, 576, 61507, 702, 264, 1990, 63141, 18202, 2598, 11249, 38554, 13, 576, 11249, 38554, 702, 70928, 892, 2138, 279, 8317, 315, 3684, 504, 4766, 279, 61507, 311, 1181, 4889, 11, 429, 374, 11, 311, 279, 9503, 98605, 10530, 320, 8206, 582, 686, 3061, 911, 304, 3772, 220, 20, 13, 17, 13, 19, 568, 576, 61507, 5610, 82081, 11, 892, 525, 9434, 438, 20589, 34731, 14389, 1172, 979, 279, 2779, 374, 911, 311, 21749, 13, 34218, 57275, 6644, 1995, 369, 41822, 315, 5766, 504, 6562, 311, 1790, 9471, 304, 279, 1352, 315, 15552, 320, 1912, 60163, 461, 749, 451, 22147, 292, 49134, 8, 34615, 13, 34218, 57275, 525, 23415, 315, 15552, 323, 12833, 13, 15552, 34615, 6644, 279, 1995, 5871, 369, 49353, 323, 87071, 7761, 13, 54450, 20632, 315, 15552, 525, 2598, 20727, 13, 758, 264, 2779, 892, 374, 537, 49702, 11, 419, 15552, 374, 3042, 438, 949, 315, 21372, 14768, 3684, 13, 34218, 14768, 3684, 374, 9434, 438, 1197, 38940, 3072, 315, 4516, 1075, 14389, 13, 42533, 279, 2779, 374, 911, 311, 21749, 11, 279, 21372, 14768, 3684, 5221, 38333, 1119, 82081, 13, 576, 61507, 11088, 264, 8622, 3476, 304, 34593, 38556, 11, 279, 1882, 553, 892, 264, 3175, 2779, 64828, 323, 7586, 1378, 501, 7761, 13, 1084, 1083, 11088, 264, 16587, 949, 11, 3156, 448, 279, 4573, 11, 304, 25597, 279, 1616, 279, 2779, 686, 2225, 323, 1128, 1352, 432, 686, 30224, 518, 47161, 11, 553, 44990, 279, 11483, 7488, 315, 279, 2779, 13, 758, 1045, 43204, 1075, 23157, 11, 279, 11249, 5537, 315, 279, 2779, 1231, 387, 30455, 4512, 4152, 311, 279, 19265, 315, 264, 11249, 38554, 13, 15132, 458, 5614, 11249, 5537, 8482, 1172, 30384, 292, 32869, 374, 2598, 264, 30384, 588, 13, 15132, 43204, 11, 6693, 7761, 6853, 264, 11249, 38554, 11, 525, 2598, 462, 74, 658, 6295, 320, 1336, 27594, 476, 6028, 595, 658, 1272, 595, 658, 263, 61507, 568, 10762, 13664, 448, 7761, 3432, 264, 11249, 38554, 525, 2598, 384, 3101, 658, 6295, 13, 1298, 74, 658, 14212, 7761, 320, 4060, 23095, 13, 220, 20, 13, 19, 8, 1083, 6853, 1429, 315, 279, 1008, 9503, 98605, 10530, 292, 1240, 2387, 642, 3042, 304, 384, 3101, 658, 14212, 7761, 13, 8999, 315, 279, 5746, 315, 1741, 1240, 2387, 642, 525, 1083, 10660, 553, 30455, 38333, 5479, 315, 279, 9503, 98605, 10530, 320, 4060, 3772, 220, 20, 13, 17, 13, 19, 568, 576, 36733, 5127, 24705, 304, 7249, 1872, 17556, 462, 74, 658, 14212, 23157, 374, 5815, 448, 30719, 276, 782, 64535, 4342, 320, 21250, 1075, 14389, 8, 714, 537, 448, 87147, 3365, 438, 304, 384, 3101, 658, 14212, 7761, 320, 4060, 3772, 220, 20, 13, 17, 13, 20, 568, 63105, 57275, 64532, 38554, 13972, 7002, 451, 22147, 588, 23095, 13, 220, 20, 13, 19, 1298, 74, 658, 14212, 2779, 220, 20, 13, 17, 13, 19, 29569 ]	[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]

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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