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1. A
   $\sin^{-1}(\tan r')$
2. B
   $\sin^{-1}(\tan r)$
3. C
   $\tan^{-1}(\sin i)$
4. D
   $\cot^{-1}(\tan i)$

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

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

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1. A
   the mean speed of the gas molecules
2. B
   mean of the square of the speed of the gas molecules
3. C
   the square of the mean speed of the gas molecules
4. D
   the root mean square speed of the gas molecules

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1. A
   $\frac{I}{5}$
2. B
   $\frac{I}{6}$
3. C
   $\frac{I}{32}$
4. D
   $\frac{I}{64}$

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1. A
   $45\times10^{-4}$ m$^3$
2. B
   $54\times10^{-4}$ m$^3$
3. C
   $34\times10^{-4}$ m$^3$
4. D
   $64\times10^{-4}$ m$^3$

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1. A
   $\frac{BLV}{R}$
2. B
   $\frac{B^2L^2V^2}{R^2}$
3. C
   $\frac{BLV}{R^2}$
4. D
   $\frac{B^2L^2V^2}{R}$

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1. A
   $n^4$
2. B
   $n^{-4}$
3. C
   $n^2$
4. D
   $n^{-2}$

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1. A
   0.3
2. B
   0.4
3. C
   0.5
4. D
   0.6

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1. A
   6.5 A from O to P
2. B
   9 A from P to O
3. C
   10.5 A from P to O
4. D
   11.5 A from O to P

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1. A
   $1240\,\Omega$ in series
2. B
   $2480\,\Omega$ in series
3. C
   $2480\,\Omega$ in parallel
4. D
   $20\,\Omega$ in parallel

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1. A
   0.4 s
2. B
   0.5 s
3. C
   0.8 s
4. D
   1.0 s

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1. A
   Both A and B are wrong
2. B
   Both A and B are correct
3. C
   A is wrong and B is correct
4. D
   A is correct and B is wrong

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

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1. A
   50 Hz, 50 Hz
2. B
   100 Hz, 100 Hz
3. C
   50 Hz, 100 Hz
4. D
   100 Hz, 50 Hz

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1. A
   $2\pi\sqrt{\frac{2R}{g}}$
2. B
   $4\pi\sqrt{\frac{2R}{g}}$
3. C
   $2\pi\sqrt{\frac{R}{g}}$
4. D
   $8\pi\sqrt{\frac{R}{g}}$

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

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1. A
   $\frac{E}{2\pi r m}$
2. B
   $\frac{E}{6\pi r m}$
3. C
   $\frac{E}{8\pi r m}$
4. D
   $\frac{E}{4\pi r m}$

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1. A
   10 V
2. B
   90 V
3. C
   1000 V
4. D
   3000 V

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

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1. A
   the width of the depletion layer decreases
2. B
   the width of the depletion layer increases
3. C
   the number of minority charge carriers increase
4. D
   the number of majority charge carriers increase

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1. A
   current is maximum when $\omega^2 = \frac{1}{LC}$
2. B
   current is zero
3. C
   voltage is minimum when $\omega^2 = \frac{1}{LC}$
4. D
   voltage is maximum when $\omega^2 = \frac{1}{LC}$

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

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1. A
   $7.22 \times 10^{-6}$ J
2. B
   $13.0 \times 10^{-5}$ J
3. C
   $2.88 \times 10^{-5}$ J
4. D
   $5.76 \times 10^{-5}$ J

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1. A
   the field is zero but potential is not zero
2. B
   the field is non-zero but the potential is zero
3. C
   both, field and potential are zero
4. D
   both, field and potential are non-zero

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