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96. In triangle $A B C, \frac{\sin A+\sin B+\sin C}{\sin A+\sin B-\sin C}$ is equal to
a. $\tan \frac{A}{2} \cot \frac{B}{2}$
b. $\cot \frac{A}{2} \tan \frac{B}{2}$
c. $\cot \frac{A}{2} \cot \frac{B}{2}$
d. $\tan \frac{A}{2} \tan \frac{B}{2}$ | 1 |
9.15 Use the mirror equation to deduce that:
(a) an object placed between $f$ and $2 f$ of a concave mirror produces a real image beyond 2 f .
(b) a convex mirror always produces a virtual image independent of the location of the object.
(c) the virtual image produced by a convex mirror is always diminished in size and is located between the focus and the pole . (d) an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.
[Note: This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.] | 1 |
Why was China never ruled by British or any other colonial powers? | 0 |
15. Choose the correct option(s) that give(s) an aromatic compound as the major product.
[Adv. 2019]
(a) $\xrightarrow{\mathrm{Br}} \xrightarrow{\mathrm{NaOEt}}$
(b)
(c)
(d)
 | 1 |
How can I get an FMCG distributor or a wholesaler to notice my product? | 0 |
1. If $z_{1}=a+i b$ and $z_{2}=c+i d$ are complex numbers such that $\left|z_{1}\right|=\left|z_{2}\right|=1$ and $\operatorname{Re}\left(z_{1} \bar{z}_{2}\right)=0$, then the pair of complex numbers $\omega_{1}=a+i c$ and $\omega_{2}=b+i d$ satisfies
a. $\left|\omega_{1}\right|=1$
b. $\left|\omega_{2}\right|=1$
c. $\operatorname{Re}\left(\omega_{1} \bar{\omega}_{2}\right)=0$
d. $\omega_{1} \bar{\omega}_{2}=0$ | 1 |
What are good fantasy & adventure books to read? | 0 |
How do I integrate 0 to π log (1+sin(x)) dx? | 0 |
3. Two identical blocks of mass $0.5 \mathrm{~kg}$ each are shown in figure. A massless elastic spring is connected with $A$. $B$ is moving towards $A$ with kinetic energy of $4 \mathrm{~J}$. Match the following two columns. Neglect friction.
| | Column I | Column II |
| :---: | :---: | :---: |
| (a) | Initial momentum of $B$ | (p) zero |
| (b) | Momentum of centre of mass of <br> two blocks | (q) $1 \mathrm{~kg} \cdot \mathrm{ms}^{-1}$ |
| (c) | Momentum of $A$ at maximum <br> compression | (r) $2 \mathrm{~kg} \cdot \mathrm{ms}^{-1}$ |
| (d) | Momentum of $B$ when spring is <br> relaxed after compression | (s) $4 \mathrm{~kg}-\mathrm{ms}^{-1}$ | | 1 |
How is life in TCS? | 0 |
What should I do for weight loss? | 0 |
6. The bond energy (in kcal $\mathbf{m o l}^{-1}$ ) of a $\mathrm{C}-\mathrm{C}$ single bond is approximately
(a) 1
(b) 10
(c) 100
(d) 1000 | 1 |
Example 2.44 $\lim _{x \rightarrow \infty} x^{1 / x}$ equals to
a. 0
b. 1
c. $e$
d. $\infty$. | 1 |
12. If $\cos (x+\pi / 3)+\cos x=a$ has real solutions, then
a. number of integral values of $a$ are 3
h sum of number of integral values of $a$ is 0
c. when $a=1$, number of solutions for $x \in[0,2 \pi]$ are 3
d when $a=1$, number of solutions for $x \in[0,2 \pi]$ are 2 | 1 |
Is it legal for officers to record a statement from my disabled daughter without me knowing? | 0 |
7. Find the value of $11^{2}+12^{2}+13^{2}+\cdots+20^{2}$ | 1 |
20. If a circle of constant radius $3 k$ passes through the origin ' $O$ ' and meets co-ordinate axes at $A$ and $B$, then the locus of the centroid of the triangle $O A B$ is
a. $x^{2}+y^{2}=(2 k)^{2}$
b. $x^{2}+y^{2}=(3 k)^{2}$
c. $x^{2}+y^{2}=(4 k)^{2}$
d. $x^{2}+y^{2}=(6 k)^{2}$ | 1 |
Where are you from, and how many languages can you speak? | 0 |
What is the best way to create a Pinger account? | 0 |
Is there a way to get paid Windows Phone apps for free, just like how Android has Blackmarket Alpha? | 0 |
What are sexual attraction. behavior, and idenity components of? | 0 |
What will happen if Donald Trump wins the election? | 0 |
what did the "Jazz Age" usher in? | 0 |
The Jawaharlal Nehru Stadium is located in which Indian city? | 0 |
22. The reaction of white phosphorus with aqueous $\mathrm{NaOH}$ gives phosphine along with another phosphorus containing compound. The reaction type; the oxidation states of phosphorus in phosphine and the other product are respectively
(a) redox reaction; -3 and -5
(b) redox reaction; +3 and +5
(c) disproportionation reaction; -3 and +5
(d) disproportionation reaction; -3 and +3 | 1 |
24. Tangents to parabola $y^{2}=4 x$ at $A$ and $C$ intersect at point $D$ and tangents to parabola $y^{2}=-8(x-a)$ intersect at point $E$, then the area of quadrilateral $D A E C$ is
a. $96 \sqrt{2}$
b. $48 \sqrt{3}$
c. $54 \sqrt{5}$
d. $36 \sqrt{6}$ | 1 |
In what area did the Indian Kings contain the Arabs? | 0 |
Ex. 3. A gas cylinder containing cooking gas can withstand a pressure of 14.9 atm . The pressure gauge of cylinder indicates 12 atm at $27^{\circ} \mathrm{C}$. Due to sudden fire in the building, its temperature starts rising. At what temperature the cylinder will explode? | 1 |
Is Run Ze Cao's falsification of Einstein's relativity valid? | 0 |
How do I make my own app? | 0 |
Are "suggested people you may know" on Facebook people that have looked at your page? | 0 |
1. $\int \frac{d x}{x^{2}\left(1+x^{5}\right)^{4 / 5}}$ | 1 |
When did England become Great Britain? | 0 |
Donald Trump or Hillary Clinton? Why? | 0 |
Would it be beneficial to do cocaine before interviewing for a sales position? | 0 |
2. What is the type of conjugation for the given reaction?
(A) Hyperconjugation
(B) Simple Conjugation
(C) Homoconjugation
(D) Double hyperconjugation | 1 |
Is Cambodia experiencing climate-change? | 0 |
59. White phosphorus $\left(\mathrm{P}_{4}\right)$ has
(a) six P-P single bonds
(b) four P-P single bonds
(c) four lone pairs of electrons
(d) PPP angle of $60^{\circ}$ | 1 |
What would Special Education usually only apply to in the early years of schooling in the U.S? | 0 |
75. A function $f$ is continuous for all $x$ (and not every where zero) such that $f^{2}(x)=\int_{0}^{x} f(t) \frac{\cos t}{2+\sin t} d t$, then $f(x)$ is
a. $\frac{1}{2} \ln \left(\frac{x+\cos x}{2}\right) ; x \neq 0$
b. $\frac{1}{2} \ln \left(\frac{3}{2+\cos x}\right) ; x \neq 0$
c. $\frac{1}{2} \ln \left(\frac{2+\sin x}{2}\right) ; x \neq n \pi, n \in I$
d. $\frac{\cos x+\sin x}{2+\sin x} ; x \neq n \pi+\frac{3 \pi}{4}, n \in I$ | 1 |
53. The first ionisation potential of Na is 5.1 eV . The value of electron gain enthalpy of $\mathrm{Na}^{+}$will be
(a) -2.55 eV
(b) -5.1 eV
(c) -10.2 eV
(d) +2.55 eV | 1 |
25. The potential difference between points $A$ and $B$, in a section of a circuit shown, is
(a) 5 volt
(b) 1 volt
(c) 10 volt
(d) 17 volt | 1 |
39. For any integer $n$, the integral $\int_{0}^{\pi} e^{\cos ^{2} x} \cos ^{3}(2 n+1) x d x$ has the value
(a) $\pi$
(b) 1
(c) 0
(d) None of these | 1 |
41. Give reasons for the following :
(i) Sulphur dioxide is a more powerful reducing agent in an alkaline medium than in acidic medium.
[1992 - 1 Mark]
(ii) Valency of oxygen is generally two whereas sulphur shows valency of two, four and six. [1988 - 1 Mark]
(iii) Sulphur melts to a clear mobile liquid at $119^{\circ} \mathrm{C}$, but on further heating above $160^{\circ} \mathrm{C}$, it becomes viscous. | 1 |
13. If ' $K$ ' is the number of ways in which we can choose 5 letters from the word INTERNATIONAL then-
(a) K is a three digit number
(b) K is divisible by 4
(c) K is divisible by 11
(d) k is divisible by 9 | 1 |
18. The area of the loop described as $x=\frac{t}{3}(6-t), y=\frac{t^{2}}{8}(6-t)$ is
a. $\frac{27}{5}$ sq. units
b. $\frac{24}{5}$ sq. units
c. $\frac{27}{6}$ sq. units
d $\frac{21}{5}$ sq. units | 1 |
What reserves are abundant in Southeast Asia? | 0 |
69. The least and the greatest values of $\left(\sin ^{-1} x\right)^{3}+\left(\cos ^{-1} x\right)^{3}$ are
a. $\frac{-\pi}{2}, \frac{\pi}{2}$
h. $\frac{-\pi^{3}}{8}, \frac{\pi^{3}}{8}$
c. $\frac{\pi^{3}}{32}, \frac{7 \pi^{3}}{8}$
d none of these | 1 |
Are there any smoking areas at UCLA dorms? | 0 |
12. When the trolley shown in figure is given a horizontal acceleration $a$, the pendulum bob of mass $m$ gets deflected to a maximum angle $\theta$ with the vertical. At the position of maximum deflection, the net acceleration of the bob with respect to trolley is
(a) $\sqrt{g^{2}+a^{2}}$
(b) $a \cos \theta$
(c) $g \sin \theta-a \cos \theta$
(d) $a \sin \theta$
 | 1 |
How many main stations of the Northern Railway serve the New Delhi area? | 0 |
When did Vitruvius write his canons? | 0 |
(iv) Amminebromidochloridonitrito-N-platinate(II) | 1 |
31. If $\operatorname{cosec} \theta-\cot \theta=q$, then the value of $\operatorname{cosec} \theta$ is
a. $q+\frac{1}{q}$
b. $q-\frac{1}{q}$
c. $\frac{1}{2}\left(q+\frac{1}{q}\right)$
d. none of these | 1 |
8. A charged particle revolves in circular path in uniform magnetic field after accelerating by a potential difference of $V$ volts. Choose the correct options if $V$ is doubled.
(a) kinetic energy of particle will become two times
(b) radius in circular path will become two times
(c) radius in circular path will become $\sqrt{2}$ times
(d) angular velocity will remain unchanged | 1 |
1.
$\begin{aligned} & x+2 y=2 \\ & 2 x+3 y=3\end{aligned}$ | 1 |
43 A radioactive sample intended for irradiation of a hospital patient is prepared at a nearby laboratory. The sample has a halflife of 83.61 h . What should its initial activity be if its activity is to be $7.4 \times 10^{8} \mathrm{~Bq}$ when it is used to irradiate the patient 24 h later? | 1 |
17. The figure shows a circular region of radius $R$ occupied by a time varying
magnetic field $\mathbf{B}(t)$ such that $\frac{d B}{d t}<0$. The magnitude of induced electric field at
the point $P$ at a distance $r<R$ is
$\begin{array}{ll}\text { (a) decreasing with } r & \text { (b) increasing with } r\end{array}$
(a) decreasing with $r$
(d) varying as $r^{-2}$ | 1 |
3. In which of the following cases the centre of mass of a rod is certainly not at its centre?
(a) the density continuously increases from left to right
(b) the density continuously decreases from left to right
(c) the density decreases from left to right upto the centre and then increases
(d) the density increases from left to right upto the centre and then decreases. | 1 |
12. The reaction $X \rightarrow Y$ is an exothermic reaction. Activation energy of the reaction for $\mathrm{X}$ into $\mathrm{Y}$ is $150 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Enthalpy of reaction is 135 $\mathrm{kJ} \mathrm{mol}^{-1}$. The activation energy for the reverse reaction, $\mathrm{Y} \rightarrow \mathrm{X}$ will be :
(a) $280 \mathrm{~kJ} \mathrm{~mol}^{-1}$
(b) $285 \mathrm{~kJ} \mathrm{~mol}^{-1}$
(c) $270 \mathrm{~kJ} \mathrm{~mol}^{-1}$
(d) $15 \mathrm{~kJ} \mathrm{~mol}^{-1}$ | 1 |
34. The area bounded by the curve $f(x)=x+\sin x$ and its inverse function between the ordinates $x=0$ and $x=2 \pi$ is
a. $4 \pi$ sq. units
b. $8 \pi$ sq. units
c. 4 sq. units
d. 8 sq. units | 1 |
Do I need to watch previous Star Wars films to watch Star Wars: The Force Awakens? | 0 |
What type of music was Date Records known for? | 0 |
What is the biological interaction where a predator feeds on its prey called? | 0 |
(iv) The square of a number is an even number. | 1 |
Slow wave sleep is also known as what? | 0 |
2. Two particles of masses $M$ and $2 M$, moving as shown, with speeds of $10 \mathrm{~m} / \mathrm{s}$ and $5 \mathrm{~m} / \mathrm{s}$, collide elastically at the origin. After the collision, they move along the indicated directions with speed $v_{1}$ and $v_{2}$ are nearly
(a) $6.5 \mathrm{~m} / \mathrm{s}$ and $3.2 \mathrm{~m} / \mathrm{s}$
(b) $3.2 \mathrm{~m} / \mathrm{s}$ and $6.3 \mathrm{~m} / \mathrm{s}$
(c) $3.2 \mathrm{~m} / \mathrm{s}$ and $12.6 \mathrm{~m} / \mathrm{s}$
(d) $6.5 \mathrm{~m} / \mathrm{s}$ and $6.3 \mathrm{~m} / \mathrm{s}$ | 1 |
How do I publish a book with no money? | 0 |
35. An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency $264 \mathrm{~Hz}$, if the length of the column in $\mathrm{cm}$ is (Speed of sound in air $=330 \mathrm{~m} / \mathrm{s}$ )
(a) 31.25
(b) 62.50
(c) 93.75
(d) 125 | 1 |
Problem 6.12
Calculate $\Delta_{r} G^{\ominus}$ for conversion of oxygen to ozone, $3 / 2 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{O}_{3}(\mathrm{~g})$ at 298 K . if $K_{p}$ for this conversion is $2.47 \times 10^{-29}$. | 1 |
36. ${ }_{90}^{232} \mathrm{Th}$ disintegrates to ${ }_y^x \mathrm{~Pb}$ by emitting six $\alpha$ - and four $\beta$-particles. Find $x$ and $y$.
$(208,82)$ | 1 |
1. Which of the following represent incorrectly named IUPAC compound?
(A) $\mathrm{CH}_{3} \mathrm{COC}_{6} \mathrm{H}_{5} \longrightarrow$ 1-Phenylethanone
(B) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COCH}\left(\mathrm{CH}_{3}\right)_{2} \longrightarrow$ 3-Hexanone
(C) $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHCOCH}\left(\mathrm{CH}_{3}\right)_{2} \longrightarrow$ 2, 4-Dimethyl 3-Pentanone
(D) $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COC}_{6} \mathrm{H}_{5} \longrightarrow$ Diphenyl methanone | 1 |
5. Equation of a common tangent to the circle, $x^{2}+y^{2}-6 x=0$ and the parabola, $y^{2}=4 x$, is
(a) $\sqrt{3} y=3 x+1$
(b) $2 \sqrt{3} y=12 x+1$
(c) $\sqrt{3} y=x+3$
(d) $2 \sqrt{3} y=-x-12$ | 1 |
Read the following statement-1(Asseration/Statement) and Statement -2 (Reason/Explanation) and answer as per the options given below: (a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (c) Statement-1 is True, Statement-2 is False (d) Statement-1 is False, Statement-2 is True71. Statement-1 : $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{NO}\right] \mathrm{SO}_{4}$ is paramagnetic. Statement-2 : The $\mathrm{Fe}$ in $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{NO}\right] \mathrm{SO}_{4}$ has three unpaired electrons. | 1 |
Why is China blocking the move to ban Masood Azhar at UN? | 0 |
Time is money.Can some one explain, how it works? | 0 |
How do you add subtext to a question using a PC? | 0 |
21. If one of the vertices of the square circumscribing the circle $|z-1|=\sqrt{2}$ is $2+\sqrt{3} i$, find the other vertices of the square | 1 |
8. The de Broglie wavelength of a car of mass $1000 \mathrm{~kg}$ and velocity $36 \mathrm{~km} / \mathrm{hr}$ is :
(a) $6.626 \times 10^{-34} \mathrm{~m}$
(b) $6.626 \times 10^{-38} \mathrm{~m}$
(c) $6.626 \times 10^{-31} \mathrm{~m}$
(d) $6.626 \times 10^{-30} \mathrm{~m}$ | 1 |
38. Compound (A) gives positive Lucas test in 5 minutes. When 6 g of $(\mathrm{A})$ is treated with Na metal, 1120 mL of $\mathrm{H}_{2}$ is evolved at STP. Assuming (A) to contain one atom of oxygen per molecule, write the structural formula of (A).
$\left[\mathrm{CH}_{3} \cdot \mathrm{CH}(\mathrm{OH}) \cdot \mathrm{CH}_{3}\right]$ | 1 |
Where can we get medical reports in Delhi? | 0 |
41. The hydrogen bond is strongest in :
(a) $\mathrm{O}-\mathrm{H} \ldots \ldots \ldots \ldots . \mathrm{S}$
(b) $\mathrm{S}-\mathrm{H} \ldots \ldots \ldots \ldots . . \mathrm{O}$
(c) $\mathrm{F}-\mathrm{H} . \ldots \ldots \ldots . . \mathrm{F}$
(d) $\mathrm{F}-\mathrm{H} . \ldots \ldots \ldots . . . \mathrm{O}$ | 1 |
4. Solve the system of the equations:
$a x+b y+c z=d$
$a^{2} x+b^{2} y+c^{2} z=d^{2}$
$a^{3} x+b^{3} y+c^{3} z=d^{3}$
Will the solution always exist and be unique? | 1 |
Example 22.14 A body cools in 10 minutes from $60^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$. What will be its temperature after next 10 minutes? The temperature of the surroundings is $10^{\circ} \mathrm{C}$. | 1 |
29. In a first order reaction the concentration of reactant decreases from $800 \mathrm{~mol} / \mathrm{dm}^{3}$ to $50 \mathrm{~mol} / \mathrm{dm}^{3}$ in $2 \times 10^{4} \mathrm{sec}$. The rate constant of reaction in $\mathrm{sec}^{-1}$ is:
(a) $2 \times 10^{4}$
(b) $3.45 \times 10^{-5}$
(c) $1.386 \times 10^{-4}$
(d) $2 \times 10^{-4}$ | 1 |
What are some good ideas for an event in a fresher's party? | 0 |
Ex. 7.0 .36 g of an organic compound containing sulphur produced $\mathrm{H}_{2} \mathrm{SO}_{4}$ by Carius method, which on treatment with $\mathrm{BaCl}_{2}$ produced quantitatively 0.2330 g of $\mathrm{BaSO}_{4}$. Calculate the percentage of S in the compound.
$$
(\mathrm{Ba}=137, \mathrm{~S}=32, \mathrm{O}=16)
$$ | 1 |
3. The correct name of the following polymer is:
[Main April 12, 2019 (II)]
(a) Polyisobutane
(b) Polytert-butylene
(c) Polyisoprene
(d) Polyisobutylene | 1 |
How did Ankita Sarkar prepare for CMI Entrance exam? What books did she use? | 0 |
What universities does Aspen Tech recruit new grads from? What majors are they looking for? | 0 |
13. If $\left(a x^{2}+c\right) y+\left(a^{\prime} x^{2}+c\right)=0$ and $x$ is a rational function of $y$ and $a c$ is negative, then
a. $a c^{\prime}+a^{\prime} c=0$
b. $a / a^{\prime}=c / c^{\prime}$
c. $a^{2}+c^{2}=a^{\prime 2}+c^{\prime 2}$
d. $a a^{\prime}+c c^{\prime}=1$ | 1 |
7. The potential energy of a 4 kg particle free to move along the $x$-axis is given by
$$
\mathrm{U}(\mathrm{x})=\frac{x^{3}}{3}-\frac{5 x^{2}}{2}+6 x+3
$$
Total mechanical energy of the particle is 17 J . Then the maximum kinetic energy is :
(a) 10 J
(b) 2 J
(c) 9.5 J
(d) 0.5 J | 1 |
Who are the most followed people on Quora? Why do they have so many followers? | 0 |
7. The temperature of the two outer surfaces of a composite slab consisting of two materials having coefficients of thermal conductivity $K$ and $2 K$ and thickness $x$ and $4 x$ respectively are $T_{2}$ and $T_{1}\left(T_{2}>T_{1}\right)$. The rate of heat transfer through the slab in steady state is $\frac{A K\left(T_{2}-T_{1}\right)}{x} f$. where, $f$ is equal to
(a) 1
(b) $1 / 2$
(c) $2 / 3$
(d) $1 / 3$ | 1 |
14. The maximum value of $f(x)=\tan ^{-1}\left(\frac{(\sqrt{12}-2) x^{2}}{x^{4}+2 x^{2}+3}\right)$ is
a. $18^{\circ}$
b $36^{\circ}$
c. $22.5^{\circ}$
d $15^{\circ}$ | 1 |
1. If $P_{1}$ has co-ordinates $(1,1)$, then the sum $\lim _{n \rightarrow \infty} \sum_{r=1}^{n} \frac{1}{x_{n}}$ is (where $x_{1}, x_{2}, \ldots$, are abscissas of $P_{1}, P_{2}, \ldots$, respectively)
a. $-2 / 3$
b. $1 / 3$
c. $1 / 2$.
d. $3 / 2$ | 1 |
How Indian economy got affected after ban of 500 1000 notes? | 0 |
What should I do to hack WhatsApp messages remotely? | 0 |
Will mastrubation cause hair fall? | 0 |
What is the concern in Southeast Asian region due to development & population expansion? | 0 |
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