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

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1. A
   $t_1 < t_2 < t_3$
2. B
   $t_1 > t_2 > t_3$
3. C
   $t_1 = t_2 = t_3$
4. D
   $t_1 < t_2 = t_3$

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1. A
   $V_1 = V_2 = V_3$
2. B
   $V_1 < V_2 < V_3$
3. C
   $V_1 > V_2 > V_3$
4. D
   $V_1 = V_3 > V_2$

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1. A
   2.5 W
2. B
   4.0 W
3. C
   10 W
4. D
   100 W

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1. A
   $P(I\alpha)^{-1}$
2. B
   $P^{-1}(I\alpha)^{-1}$
3. C
   $P\alpha^{-1}I$
4. D
   $PI\alpha$

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1. A
   less than the external electric field
2. B
   larger than the external electric field
3. C
   equal to the external electric field
4. D
   equal to or greater than external electric field

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

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1. A
   A=0,B=0,Y=1; A=0,B=1,Y=1; A=1,B=0,Y=1; A=1,B=1,Y=0
2. B
   A=0,B=0,Y=0; A=0,B=1,Y=0; A=1,B=0,Y=1; A=1,B=1,Y=1
3. C
   A=0,B=0,Y=0; A=0,B=1,Y=1; A=1,B=0,Y=1; A=1,B=1,Y=1
4. D
   A=0,B=0,Y=0; A=0,B=1,Y=1; A=1,B=0,Y=0; A=1,B=1,Y=1

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

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1. A
   $-13\,\text{V}$
2. B
   $13\,\text{V}$
3. C
   $-23\,\text{V}$
4. D
   $23\,\text{V}$

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

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1. A
   is increased
2. B
   is decreased
3. C
   remains the same
4. D
   becomes zero

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1. A
   $\frac{3C_1 n_1}{n_2}$
2. B
   $\frac{9n_2}{n_1}C_1$
3. C
   $\frac{3n_2}{n_1}C_1$
4. D
   $\frac{9C_1 n_1}{n_2}$

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1. A
   $\sqrt{\frac{2g}{5R}}$
2. B
   $\sqrt{\frac{3g}{5R}}$
3. C
   $\sqrt{\frac{5R}{3g}}$
4. D
   $\sqrt{\frac{3}{5}gR}$

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

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1. A
   1.3 A
2. B
   1.4 A
3. C
   1.5 A
4. D
   1.6 A

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1. A
   n-type side has lower potential than p-type side
2. B
   n-type side has same potential as p-type side
3. C
   An electric field is established at the junction such that n side is at positive voltage relative to p-side
4. D
   The potential across the junction is such that p-side is at positive voltage relative to n-side

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1. A
   $\cos^{-1}\!\left(\frac{1}{2}\right)$
2. B
   $\cos^{-1}\!\left(\frac{1}{3}\right)$
3. C
   $\cos^{-1}\!\left(\frac{1}{4}\right)$
4. D
   $\cos^{-1}\!\left(\frac{1}{6}\right)$

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1. A
   $\frac{T}{6}$
2. B
   $\frac{T}{3}$
3. C
   $\frac{T}{2}$
4. D
   $\frac{T}{12}$

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1. A
   at the mid-point of line joining the two particles
2. B
   on the line joining the two particles
3. C
   at one end of the line joining the two particles
4. D
   on the line perpendicular to the line joining the two particles

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

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1. A
   1.6 cm
2. B
   2.4 cm
3. C
   3.2 cm
4. D
   4.8 cm

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1. A
   300 K
2. B
   375 K
3. C
   400 K
4. D
   450 K

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1. A
   $119.5°$
2. B
   $180°$
3. C
   $109°$
4. D
   $107.5°$

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1. A
   $1.0 \times 10^{21}$
2. B
   $2.0 \times 10^{21}$
3. C
   $3.0 \times 10^{21}$
4. D
   $4.0 \times 10^{21}$

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