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1. A
   $\frac{\pi^2}{4}-2$
2. B
   $\frac{\pi^2}{4}+2$
3. C
   $\pi^2-e^{\pi/2}$
4. D
   $\pi^2+e^{\pi/2}$

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

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1. A
   $\frac{1}{16}$
2. B
   $\frac{9}{16}$
3. C
   $\frac{3}{4}$
4. D
   $\frac{15}{16}$

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

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

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

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1. A
   45
2. B
   75
3. C
   105
4. D
   120

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1. A
   $fg=ch$
2. B
   $gh=cf$
3. C
   $fh=cg$
4. D
   $hf=-cg$

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1. A
   $x=n\pi+\frac{\pi}{4},\,n\in\mathbb{Z}$
2. B
   $x=2n\pi+\frac{\pi}{4},\,n\in\mathbb{Z}$
3. C
   $x=n\pi+(-1)^n\frac{\pi}{4},\,n\in\mathbb{Z}$
4. D
   $x=\frac{n\pi}{2}+\frac{\pi}{8},\,n\in\mathbb{Z}$

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

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1. A
   5
2. B
   $\frac{35}{3}$
3. C
   $-\frac{35}{3}$
4. D
   $-5$

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

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

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1. A
   T, F, T.
2. B
   T, T, T.
3. C
   F, T, F.
4. D
   T, T, F.

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

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1. A
   +2q and +2q
2. B
   +q and +3q
3. C
   +q and +2q
4. D
   +2q and +3q

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1. A
   50 times
2. B
   25 times
3. C
   40 times
4. D
   100 times

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1. A
   $T_1 T_2 = 13$
2. B
   $\frac{T_1}{T_2}^4 = \frac{e_2}{e_1}$
3. C
   $\frac{T_1}{T_2} = \frac{31}{41}$
4. D
   $\frac{T_1}{T_2} = \frac{91}{41}$

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1. A
   $\frac{\mu_0 \pi (r_1+r_2)^2}{2r_2}$
2. B
   $\frac{\mu_0 \pi (r_1-r_2)^2}{2r_1}$
3. C
   $\frac{\mu_0 \pi r_1^2}{2r_2}$
4. D
   $\frac{\mu_0 \pi r_2^2}{2r_1}$

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1. A
   becomes zero
2. B
   decreases
3. C
   increases
4. D
   remains unchanged

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1. A
   $\frac{P}{Q} = \frac{R}{S_1+S_2}$
2. B
   $\frac{P}{Q} = \frac{R(S_1+S_2)}{S_1 S_2}$
3. C
   $\frac{P}{Q} = \frac{R(S_1+S_2)}{2S_1 S_2}$
4. D
   $\frac{P}{Q} = \frac{R S_1 S_2}{S_1+S_2}$

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1. A
   $\left(\frac{\rho_B}{\rho_A}\right)^{2/3}$
2. B
   $\left(\frac{\rho_A}{\rho_B}\right)^{2/3}$
3. C
   $\frac{\rho_A}{\rho_B}$
4. D
   $\frac{\rho_B}{\rho_A}$

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1. A
   12 cm
2. B
   10 cm
3. C
   6 cm
4. D
   2 cm

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1. A
   Mg
2. B
   $Mg - V\rho g$
3. C
   $Mg + \pi R^2 h\rho g$
4. D
   $\rho g(V + \pi R^2 h)$

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1. A
   $\left(\frac{\sqrt{I_2}+\sqrt{3/8}}{\sqrt{I_2}-\sqrt{3/8}}\right)^2$
2. B
   $\left(\frac{\sqrt{1/4}+\sqrt{3/8}}{\sqrt{1/4}-\sqrt{3/8}}\right)^2$
3. C
   $\frac{5}{8}$
4. D
   $\frac{8}{5}$

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