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

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1. A
   $\dfrac{13}{10}t$
2. B
   $\dfrac{13}{5}t$
3. C
   $\dfrac{10}{13}t$
4. D
   $\dfrac{5}{13}t$

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1. A
   $I_d = V_0\omega C\cos\omega t$
2. B
   $I_d = \dfrac{V_0}{\omega C}\cos\omega t$
3. C
   $I_d = \dfrac{V_0}{\omega C}\sin\omega t$
4. D
   $I_d = V_0\omega C\sin\omega t$

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

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1. A
   $4\sqrt{2}\ \Omega$
2. B
   $\dfrac{5}{\sqrt{2}}\ \Omega$
3. C
   $4\ \Omega$
4. D
   $5\ \Omega$

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1. A
   Graph (1): B increasing as a concave-up curve with r (B $\propto r^2$-like)
2. B
   Graph (2): B increasing linearly with r throughout
3. C
   Graph (3): B rising linearly up to r = R then falling as 1/r (hyperbola)
4. D
   Graph (4): B rising and saturating (concave-down) with r

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1. A
   $\lambda = \left(\dfrac{2m}{hc}\right)\lambda_d^2$
2. B
   $\lambda_d = \left(\dfrac{2mc}{h}\right)\lambda^2$
3. C
   $\lambda = \left(\dfrac{2mc}{h}\right)\lambda_d^2$
4. D
   $\lambda = \left(\dfrac{2h}{mc}\right)\lambda_d^2$

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

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1. A
   $[F][A][T]$
2. B
   $[F][A][T^2]$
3. C
   $[F][A][T^{-1}]$
4. D
   $[F][A^{-1}][T]$

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1. A
   $\dfrac{R_1}{R_2}$
2. B
   $\dfrac{R_2}{R_1}$
3. C
   $\dfrac{R_1^2}{R_2}$
4. D
   $\dfrac{R_2^2}{R_1}$

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1. A
   20 cm from the lens, it would be a real image
2. B
   30 cm from the lens, it would be a real image
3. C
   30 cm from the plane mirror, it would be a virtual image
4. D
   20 cm from the plane mirror, it would be a virtual image

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1. A
   $\dfrac{r_1}{r_2+r_3}$
2. B
   $\dfrac{r_2}{r_2+r_3}$
3. C
   $\dfrac{r_1}{r_1+r_2}$
4. D
   $\dfrac{r_2}{r_1+r_3}$

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1. A
   Waveform (1): y stays at 0 V throughout
2. B
   Waveform (2): y high (5 V) only during t1–t3, else 0 V
3. C
   Waveform (3): y stays high at 5 V throughout
4. D
   Waveform (4): y high except a low pulse in t1–t2 and t3–t4

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1. A
   25 rad/s and 75 rad/s
2. B
   50 rad/s and 25 rad/s
3. C
   46 rad/s and 54 rad/s
4. D
   42 rad/s and 58 rad/s

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1. A
   20 m/s, 5 m/s$^2$
2. B
   20 m/s, 0
3. C
   $20\sqrt{2}$ m/s, 0
4. D
   $20\sqrt{2}$ m/s, 10 m/s$^2$

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1. A
   $R\left(\dfrac{k}{1-k}\right)^2$
2. B
   $R\left(\dfrac{k}{1+k}\right)^2$
3. C
   $\dfrac{R^2 k}{1+k}$
4. D
   $\dfrac{Rk^2}{1-k^2}$

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1. A
   $\theta = \cos^{-1}\left(\dfrac{gT^2}{\pi^2 R}\right)^{1/2}$
2. B
   $\theta = \cos^{-1}\left(\dfrac{\pi^2 R}{gT^2}\right)^{1/2}$
3. C
   $\theta = \sin^{-1}\left(\dfrac{\pi^2 R}{gT^2}\right)^{1/2}$
4. D
   $\theta = \sin^{-1}\left(\dfrac{2gT^2}{\pi^2 R}\right)^{1/2}$

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1. A
   $-8\hat{i} - 8\hat{j} - 6\hat{k}$
2. B
   $-6\hat{i} - 6\hat{j} - 8\hat{k}$
3. C
   $8\hat{i} + 8\hat{j} - 6\hat{k}$
4. D
   $6\hat{i} + 6\hat{j} - 8\hat{k}$

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1. A
   0 kg m/s
2. B
   4.2 kg m/s
3. C
   2.1 kg m/s
4. D
   1.4 kg m/s

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1. A
   $\sqrt{3}\ Ia^2$ and 3 $Ia^2$
2. B
   3 $Ia^2$ and $Ia^2$
3. C
   3 $Ia^2$ and 4 $Ia^2$
4. D
   4 $Ia^2$ and 3 $Ia^2$

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1. A
   660 V
2. B
   1320 V
3. C
   1520 V
4. D
   1980 V

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1. A
   $\dfrac{1}{2}$ kg
2. B
   $\dfrac{1}{3}$ kg
3. C
   $\dfrac{1}{6}$ kg
4. D
   $\dfrac{1}{12}$ kg

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1. A
   $\dfrac{3}{4}$
2. B
   $\dfrac{7}{8}$
3. C
   $\dfrac{1}{4}$
4. D
   $\dfrac{1}{8}$

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

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1. A
   $120^\circ$
2. B
   $180^\circ$
3. C
   $60^\circ$
4. D
   $0^\circ$

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