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1. A
   inversely proportional to inductance and frequency of the alternating current
2. B
   inversely proportional to frequency of alternating current and directly proportional to inductance
3. C
   inversely proportional to inductance and directly proportional to the frequency of alternating current
4. D
   directly proportional to inductance and frequency of alternating current

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

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1. A
   Both statements A and B are wrong.
2. B
   Only the statement B is true.
3. C
   Only the statement A is true.
4. D
   Both statements A and B are true.

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

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1. A
   $250$ m$^{-1}$
2. B
   $2.5 \times 10^6$ m$^{-1}$
3. C
   $0.25 \times 10^9$ m$^{-1}$
4. D
   $2.5 \times 10^5$ m$^{-1}$

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

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1. A
   $\sqrt{\frac{m_3}{m_1}}$
2. B
   $\sqrt{\frac{m_1}{m_2}}$
3. C
   $\frac{m_1}{m_2}$
4. D
   $\sqrt{\frac{m_2}{m_1}}$

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

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1. A
   20 g
2. B
   10 g
3. C
   40 g
4. D
   5 g

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

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1. A
   decreases with increase of slit width
2. B
   may increase or decrease
3. C
   decreases with decrease of slit width
4. D
   increases with increase in slit width

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1. A
   momentum
2. B
   velocity
3. C
   acceleration
4. D
   kinetic energy

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1. A
   $\sqrt{\frac{T}{\rho g d}}$
2. B
   $\sqrt{\frac{4T}{3\rho g d}}$
3. C
   $\sqrt{\frac{3T}{4\rho g d}}$
4. D
   $\sqrt{\frac{2T}{\rho g d}}$

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1. A
   3.6 N
2. B
   2.4 N
3. C
   1.2 N
4. D
   6.0 N

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1. A
   isochoric process
2. B
   adiabatic process
3. C
   isothermal process
4. D
   isobaric process

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1. A
   7 A
2. B
   3.3 A
3. C
   2 A
4. D
   2.5 A

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

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1. A
   $6\,\Omega$
2. B
   $7\,\Omega$
3. C
   $10\,\Omega$
4. D
   $5\,\Omega$

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

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1. A
   2f
2. B
   4f
3. C
   1.5f
4. D
   2.5f

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1. A
   specific heat
2. B
   thermal capacity
3. C
   water equivalent
4. D
   temperature gradient

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1. A
   6.5 s
2. B
   20 s
3. C
   16.5 s
4. D
   10 s

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

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1. A
   $\tan^{-1}\!\left(\frac{4}{3}\right)$
2. B
   $\tan^{-1}\!\left(\frac{3}{4}\right)$
3. C
   $\tan^{-1}\!\left(\frac{3}{2}\right)$
4. D
   $\tan^{-1}\!\left(\frac{4}{5}\right)$

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1. A
   a pure direct current
2. B
   a.c. with ripples at double the input frequency
3. C
   a.c. at the same frequency as input
4. D
   pulsating d.c. at double the input frequency

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