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1. A
   $y=\sin(x+y)+c$
2. B
   $y=\tan(x+y)+c$
3. C
   $y=\tan\frac{x+y}{2}+c$
4. D
   $y=\frac{1}{2}\tan(x+y)+c$

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1. A
   $(e-1)^{2}$ sq. units
2. B
   $e^{2}-e+1$ sq. units
3. C
   $e^{2}-e+1-2\log2$ sq. units
4. D
   $e^{2}+e-2\log2$ sq. units

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

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

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1. A
   $0<x<\frac{\pi}{8}$
2. B
   $\frac{\pi}{4}<x<\frac{\pi}{2}$
3. C
   $\frac{3\pi}{8}<x<\frac{5\pi}{8}$
4. D
   $\frac{5\pi}{8}<x<\frac{3\pi}{4}$

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1. A
   $-\frac{2}{5}+\frac{4}{5}i$
2. B
   $\frac{2}{5}-\frac{4}{5}i$
3. C
   $-\frac{2}{5}-\frac{4}{5}i$
4. D
   $\frac{2}{5}+\frac{4}{5}i$

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1. A
   $\frac{1}{3(1+\tan^{3}x)}+c$
2. B
   $-\frac{1}{3(1+\tan^{3}x)}+c$
3. C
   $\frac{1}{1+\cot^{3}x}+c$
4. D
   $-\frac{1}{1+\cos^{3}x}+c$

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1. A
   $x+y+z-3=0$
2. B
   $x+y+z-2=0$
3. C
   $x+y-z-2=0$
4. D
   $x-y+z-3=0$

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1. A
   5
2. B
   7
3. C
   6
4. D
   4

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1. A
   P(0)=144/169, P(1)=24/169, P(2)=1/169
2. B
   P(0)=1/169, P(1)=144/169, P(2)=24/169
3. C
   P(0)=24/169, P(1)=1/169, P(2)=144/169
4. D
   P(0)=144/169, P(1)=1/169, P(2)=24/169

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1. A
   $\cos2\alpha$
2. B
   $\sin\alpha$
3. C
   $\cos\alpha$
4. D
   $\sin2\alpha$

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1. A
   $\left\{\frac{\pi}{3},\frac{2\pi}{3}\right\}$
2. B
   $\left\{\frac{\pi}{3},\frac{4\pi}{3}\right\}$
3. C
   $\left\{\frac{2\pi}{3},\frac{4\pi}{3}\right\}$
4. D
   $\left\{\frac{2\pi}{3},\frac{5\pi}{3}\right\}$

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1. A
   $-0.1$
2. B
   $-0.025$
3. C
   0.1
4. D
   0.025

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1. A
   5
2. B
   7
3. C
   13
4. D
   $-2$

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1. A
   1
2. B
   $-1$
3. C
   2
4. D
   $-2$

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1. A
   7
2. B
   6
3. C
   1
4. D
   7

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1. A
   4
2. B
   7
3. C
   $\sqrt{14}$
4. D
   2

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1. A
   $\sqrt{\frac{37}{10}}$
2. B
   $\sqrt{\frac{37}{10}}$
3. C
   $\sqrt{\frac{37}{10}}$
4. D
   $\sqrt{\frac{37}{10}}$

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

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1. A
   $\log\frac{x}{x^{2}-1}+c$
2. B
   $\log\frac{x^{2}-1}{x}+c$
3. C
   $\log(x^{2}-1)+c$
4. D
   $\log\frac{x^{2}+1}{x}+c$

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1. A
   $\frac{8}{11}$
2. B
   $\frac{4}{11}$
3. C
   $-\frac{8}{11}$
4. D
   $-\frac{4}{11}$

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1. A
   If the surface area does not increase, then the pressure does not decrease.
2. B
   If the pressure decreases, then the surface area increases.
3. C
   If the pressure does not decrease, then the surface area does not increase.
4. D
   If the surface area does not increase, then the pressure decreases.

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

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1. A
   If both x and y are odd integers, then xy is odd.
2. B
   If both x and y are even integers, then xy is even.
3. C
   If x or y is an odd integer, then xy is odd.
4. D
   If both x and y are not odd integers, then the product xy is not odd.

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1. A
   0
2. B
   $-1$
3. C
   1
4. D
   2

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