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1. A
   $8\pi R^{2}T$
2. B
   $16\pi R^{2}T$
3. C
   $34\pi R^{2}T$
4. D
   $36\pi R^{2}T$

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1. A
   'AND', 'OR'
2. B
   'OR', 'NOR'
3. C
   'NAND', 'NOR'
4. D
   'NAND', 'OR'

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1. A
   $\frac{Vl_{1}}{2l^{2}}$
2. B
   $\frac{Vl_{1}}{2l^{2}}$
3. C
   $\frac{Vl_{1}}{4l^{2}}$
4. D
   $\frac{Vl_{2}}{2l_{1}}$

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1. A
   $48$ H
2. B
   $12$ H
3. C
   $4\pi \times 10^{-2}$ H
4. D
   $8\pi \times 10^{-2}$ H

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1. A
   $\frac{3}{7}$
2. B
   $\frac{2}{7}$
3. C
   $\frac{4}{7}$
4. D
   $\frac{5}{7}$

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1. A
   0.2 A
2. B
   0.8 A
3. C
   1 A
4. D
   1.2 A

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1. A
   $W_{1}=W_{2}=W_{3}$
2. B
   $W_{1}<W_{2}<W_{3}$
3. C
   $W_{1}>W_{2}<W_{3}$
4. D
   $W_{1}<W_{2}>W_{3}$

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1. A
   1.5 cm
2. B
   2 cm
3. C
   3 cm
4. D
   4.0 cm

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1. A
   the intensity of the maxima decreases and the minima has zero intensity.
2. B
   the intensity of maxima decreases and that of the minima increases.
3. C
   the intensity of the maxima increases and the minima has zero intensity.
4. D
   the intensities of both the maxima and the minima increase.

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1. A
   $\frac{\mu_{0}}{4\pi}\frac{I}{b^{2}}$
2. B
   $\frac{\mu_{0}}{4\pi}\frac{I^{2}}{b^{2}}$
3. C
   $\frac{\mu_{0}}{4\pi}\frac{I^{2}}{b}$
4. D
   $\frac{\mu_{0}}{4\pi}\frac{2I^{2}}{b}$

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1. A
   $\tan^{-1}(0)$
2. B
   $\tan^{-1}\!\left(\frac{1}{\sqrt{3}}\right)$
3. C
   $\tan^{-1}(1)$
4. D
   $\tan^{-1}(\sqrt{3})$

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

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1. A
   $2\sin\frac{30^{\circ}+\delta_{m}}{2}$
2. B
   $2\sqrt{3}\sin\frac{30^{\circ}+\delta_{m}}{2}$
3. C
   $2\sin\frac{60^{\circ}+\delta_{m}}{2}$
4. D
   $2\sqrt{3}\sin\frac{60^{\circ}+\delta_{m}}{2}$

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1. A
   350 J
2. B
   300 J
3. C
   250 J
4. D
   200 J

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

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1. A
   increases.
2. B
   decreases.
3. C
   does not change.
4. D
   is zero.

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1. A
   $\frac{BR^{3}}{2\pi\mu_{0}}$
2. B
   $\frac{2\pi BR^{3}}{\mu_{0}}$
3. C
   $\frac{BR^{2}}{2\pi\mu_{0}}$
4. D
   $\frac{2\pi BR^{2}}{\mu_{0}}$

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1. A
   $\cos^{-1}(1)$
2. B
   $\cos^{-1}\!\left(\frac{\sqrt{3}}{2}\right)$
3. C
   $\cos^{-1}\!\left(\frac{1}{\sqrt{2}}\right)$
4. D
   $\cos^{-1}\!\left(\frac{1}{2}\right)$

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1. A
   6 mm
2. B
   4 mm
3. C
   1.5 mm
4. D
   0.9 mm

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1. A
   8.5%
2. B
   12.5%
3. C
   25%
4. D
   87.5%

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1. A
   $0.2\pi$ s
2. B
   $0.3\pi$ s
3. C
   $0.4\pi$ s
4. D
   $0.5\pi$ s

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

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1. A
   glass to air
2. B
   air to glass
3. C
   glass to water
4. D
   water to glass

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1. A
   $\frac{11}{3}R$
2. B
   $\frac{23}{7}R$
3. C
   $\frac{16}{7}R$
4. D
   $\frac{23}{3}R$

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1. A
   remain same.
2. B
   becomes half.
3. C
   becomes four time.
4. D
   becomes quarter.

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