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

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1. A
   2
2. B
   $\frac{2\sin20^\circ}{\sin40^\circ}$
3. C
   4
4. D
   $\frac{4\sin20^\circ}{\sin40^\circ}$

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

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

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

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

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1. A
   $x\log|y|=x-1$
2. B
   $x\log|y|=-2(x-1)$
3. C
   $x\log|y|=2(x-1)$
4. D
   $x^2\log|y|=-2(x-1)$

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1. A
   $\frac{n(n+1)(2n+1)}{4}$
2. B
   $\frac{n(n+1)(2n+1)}{6}$
3. C
   $\frac{n(n+1)(2n+1)}{2}$
4. D
   $\frac{n(n+1)(2n+1)}{3}$

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1. A
   $\frac{10}{3^5}$
2. B
   $\frac{17}{3^5}$
3. C
   $\frac{13}{3^5}$
4. D
   $\frac{11}{3^5}$

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

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

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

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

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

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1. A
   will decrease.
2. B
   will increase.
3. C
   will not change.
4. D
   may increase or decrease depending upon the values of pressure and volume.

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1. A
   $\mu_{0} N^{2}RB$
2. B
   $\frac{RB}{2\mu_{0} N}$
3. C
   $\mu_{0} NRB$
4. D
   $\frac{2RB}{\mu_{0} N}$

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1. A
   2
2. B
   4
3. C
   28
4. D
   32

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1. A
   $1.8\times10^{5}$ volt
2. B
   $3.6\times10^{5}$ volt
3. C
   $5.4\times10^{5}$ volt
4. D
   $7.2\times10^{5}$ volt

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1. A
   $2\pi$
2. B
   $\pi$
3. C
   $\sqrt{\pi^{2}+4}$
4. D
   $3\pi$

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1. A
   35 cm
2. B
   40 cm
3. C
   47 cm
4. D
   64 cm

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1. A
   $200\,\Omega,\,0.55\text{ H}$
2. B
   $100\,\Omega,\,0.8\text{ H}$
3. C
   $300\,\Omega,\,1.2\text{ H}$
4. D
   $200\,\Omega,\,1.5\text{ H}$

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1. A
   $\frac{2\pi MR^{2}}{5T}$
2. B
   $\frac{4\pi MR^{2}}{5T}$
3. C
   $\frac{MR^{2}T}{2\pi}$
4. D
   $\frac{MR^{2}T}{4\pi}$

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1. A
   $n+\frac{S}{s'}$
2. B
   $\frac{S(n-1)-S'}{S'}$
3. C
   $\frac{(n+1)S}{s'}$
4. D
   $\frac{S(n-1)+S'}{S'}$

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1. A
   zero
2. B
   $\frac{1}{2}(m_{1}+m_{2})gt$
3. C
   $(m_{1}+m_{2})gt$
4. D
   $2(m_{1}+m_{2})gt$

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1. A
   $2\pi\times10^{-4}$
2. B
   $2.4\pi\times10^{-4}$
3. C
   $4\pi\times10^{-4}$
4. D
   $4.8\pi\times10^{-4}$

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