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1. A
   9
2. B
   $\frac{9}{4}$
3. C
   $\frac{9}{2}$
4. D
   27

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1. A
   $0 < x \leq 1$
2. B
   $0 \leq x \leq 1$
3. C
   $-\infty < x \leq 0$
4. D
   $-\infty < x < 1$

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1. A
   Increasing in $\left(-\frac{1}{2}, 1\right)$
2. B
   Decreasing in $\mathbb{R}$
3. C
   Increasing in $\mathbb{R}$
4. D
   Decreasing in $\left(-\frac{1}{2}, 1\right)$

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1. A
   x+y = c, where c is a constant of integration.
2. B
   x-y = c(xy), where c is a constant of integration.
3. C
   x+y = c(1+xy), where c is a constant of integration.
4. D
   y-x = c(1+xy), where c is a constant of integration.

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1. A
   81
2. B
   9
3. C
   5
4. D
   4

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1. A
   $\frac{3}{2}$
2. B
   $\frac{2}{3}$
3. C
   1
4. D
   $\frac{3}{4}$

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1. A
   $\frac{\pi}{4}$
2. B
   $\pi$
3. C
   $\frac{\pi}{2}$
4. D
   $2\pi$

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1. A
   4
2. B
   11
3. C
   5
4. D
   0

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1. A
   $\frac{1}{2}$
2. B
   $-\frac{1}{2}$
3. C
   $-1$
4. D
   $-\frac{1}{4}$

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1. A
   $\frac{1}{2}$ sq. units
2. B
   $\frac{1}{3}$ sq. units
3. C
   $\frac{1}{4}$ sq. units
4. D
   $\frac{1}{6}$ sq. units

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1. A
   $-\frac{1}{2}$
2. B
   $-1$
3. C
   $\frac{1}{2}$
4. D
   1

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1. A
   $\frac{1}{4}$
2. B
   $\frac{1}{2}$
3. C
   $\frac{1}{8}$
4. D
   $\frac{1}{5}$

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1. A
   a, b, c are in G.P.
2. B
   a, b, c are in H.P.
3. C
   a, b, c are in A.P.
4. D
   a, b, c are in Arithmetico Geometric Progression

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1. A
   Intersect each other and point of intersection is (2,1,3)
2. B
   Intersect each other and point of intersection is (3,2,4)
3. C
   Intersect each other and point of intersection is (-2,3,3)
4. D
   Do not intersect.

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1. A
   $\sin\frac{y}{x}=\log(x)+\frac{1}{2}$
2. B
   $\csc\frac{y}{x}=\log(x)+2$
3. C
   $\sec^2\frac{y}{x}=\log(x)+2$
4. D
   $\cos^2\frac{y}{x}=\log(x)+\frac{1}{2}$

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1. A
   $2x+y \leq 2,\; x-y \leq 1,\; x+2y \leq 8$
2. B
   $2x+y \geq 2,\; x-y \leq 1,\; x+2y \leq 8$
3. C
   $2x+y \geq 2,\; x-y \geq 1,\; x+2y \leq 8$
4. D
   $2x+y \geq 2,\; x-y \geq 1,\; x+2y \geq 8$

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1. A
   2
2. B
   6
3. C
   4
4. D
   8

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1. A
   $\tan^{-1}\frac{17}{31}$
2. B
   $\tan^{-1}\frac{19}{31}$
3. C
   $\tan^{-1}\frac{31}{17}$
4. D
   $\tan^{-1}\frac{31}{19}$

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1. A
   $-\cot(e^x)+c$, where c is a constant of integration.
2. B
   $\tan(x\cdot e^x)+c$, where c is a constant of integration.
3. C
   $\tan(e^x)+c$, where c is a constant of integration.
4. D
   $-\cot(x)\cdot e^x+c$, where c is a constant of integration.

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1. A
   $\frac{\sqrt{3}}{2}$
2. B
   $\frac{2}{\sqrt{3}}$
3. C
   $\frac{2}{\sqrt{3}}$
4. D
   $\frac{1}{2\sqrt{3}}$

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1. A
   $\lambda \cdot \sigma_x$
2. B
   $\lambda \cdot \sigma^2$
3. C
   $\lambda^2 \cdot \sigma_x$
4. D
   $\lambda^2 \cdot \sigma_x^2$

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1. A
   $\frac{\hat{i}+3\hat{j}+\hat{k}}{\sqrt{11}}$
2. B
   $\frac{\hat{i}-3\hat{j}+\hat{k}}{\sqrt{11}}$
3. C
   $\frac{\hat{i}-3\hat{j}-\hat{k}}{\sqrt{11}}$
4. D
   $\frac{\hat{i}+3\hat{j}-\hat{k}}{\sqrt{11}}$

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1. A
   $p^2-q^2$
2. B
   $4(p^2-q^2)$
3. C
   $p^2+q^2$
4. D
   $4(p^2+q^2)$

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1. A
   $\frac{2}{3}$
2. B
   $-\frac{2}{3}$
3. C
   $\frac{1}{3}$
4. D
   $-\frac{1}{3}$

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1. A
   $q$
2. B
   $(\sim p)\vee q$
3. C
   $(\sim p)\wedge q$
4. D
   $(\sim p)\vee(\sim q)$

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