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1. A
   8
2. B
   $\frac{1}{2}$
3. C
   $- \frac{15}{4}$
4. D
   $\frac{1}{8}$

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1. A
   $\left( x^{2} + y^{2} \right)^{2} - 16x^{2} + 9y^{2} = 0$
2. B
   $\left( x^{2} + y^{2} \right)^{2} - 9x^{2} + 144y^{2} = 0$
3. C
   $\left( x^{2} + y^{2} \right)^{2} - 9x^{2} - 16y^{2} = 0$
4. D
   $\left( x^{2} + y^{2} \right)^{2} - 9x^{2} + 16y^{2} = 0$

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1. A
   3
2. B
   4
3. C
   8
4. D
   2

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

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1. A
   (A)-(ii), (B)- (i), (C)-(iv), (D)-(iii)
2. B
   (A)-(ii), (B)- (iv), (C)-(i), (D)-(iii)
3. C
   (A)-(ii), (B)- (i), (C)-(iii), (D)-(iv)
4. D
   (A)-(iii), (B)- (iv), (C)-(i), (D)-(ii)

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

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

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1. A
   $194.8\text{ }nm$
2. B
   $490.7\text{ }nm$
3. C
   $913.3\text{ }nm$
4. D
   $121.8\text{ }nm$

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1. A
   a macroscopic region with consecutive magnetic diploes oriented in opposite direction.
2. B
   a macroscopic region with zero magnetization.
3. C
   a macroscopic region with saturation magnetization.
4. D
   a macroscopic region with randomly oriented magnetic dipoles.

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1. A
   $100\text{ }N$
2. B
   $50\text{ }N$
3. C
   $9.87\text{ }N$
4. D
   $0.49\text{ }N$

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1. A
   $400NM$
2. B
   $382\text{ }nm$
3. C
   $309\text{ }nm$
4. D
   $329\text{ }nm$

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1. A
   $\frac{q}{48\varepsilon_{0}}$
2. B
   $\frac{q}{8\varepsilon_{0}}$
3. C
   $\frac{q}{24\varepsilon_{0}}$
4. D
   $\frac{q}{4\varepsilon_{0}}$

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1. A
   $\frac{2}{5}\frac{v_{0}^{2}}{gsin\theta}$
2. B
   $\frac{10v_{0}^{2}}{7gsin\theta}$
3. C
   $\frac{v_{0}^{2}}{5gsin\theta}$
4. D
   $\frac{7}{10}\frac{v_{0}^{2}}{gsin\theta}$

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1. A
   its size decreases, but intensity increases
2. B
   its size increases, but intensity decreases
3. C
   its size increases, and intensity increases
4. D
   its size decreases, and intensity decreases

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1. A
   918
2. B
   1836
3. C
   $\frac{1}{1836}$
4. D
   1

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

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1. A
   $45\text{ }m$
2. B
   $35\text{ }m$
3. C
   $25\text{ }m$
4. D
   $50\text{ }m$

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1. A
   $\frac{c}{f_{c} + f_{m}}$
2. B
   $\frac{c}{f_{c} - f_{m}}$
3. C
   $\frac{C}{f_{m}}$
4. D
   $\frac{c}{f_{c}}$

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1. A
   Both statement I and statement II are false.
2. B
   Both statement I and statement II are true.
3. C
   Statement I is false but statement II is true
4. D
   Statement I is true but statement II is false.

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1. A
   $\frac{\sin^{2}\beta}{\cos^{2}\alpha}$
2. B
   $\frac{\cos^{2}\beta}{\cos^{2}\alpha}$
3. C
   $\frac{\cos\beta}{\sin\alpha}$
4. D
   $\frac{\cos\beta}{\cos\alpha}$

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1. A
   $2.5\text{ }A$
2. B
   $2\text{ }A$
3. C
   $1\text{ }A$
4. D
   $1.5\text{ }A$

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1. A
   Fermi-level of $p$ and $n$-type semiconductors will not be affected.
2. B
   Fermi-level of p-type semiconductors will go downward and Fermi-level of n-type semiconductor will go upward.
3. C
   Fermi-level of both $p$-type and n-type semiconductors will go upward for $T > T_{F}K$ and downward for $T < T_{F}K$, where $T_{F}$ is Fermi temperature.
4. D
   Fermi-level of p-type semiconductor will go upward and Fermi-level of n-type semiconductors will go downward.

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

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1. A
   $\left\lbrack {LC}^{- 1} \right\rbrack$
2. B
   $\left\lbrack M^{0}L^{0}T^{0} \right\rbrack$
3. C
   $\left\lbrack MLT^{0} \right\rbrack$
4. D
   $\left\lbrack MLT^{- 1} \right\rbrack$

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1. A
   Both statement I and statement II are true
2. B
   Both statement I and statement II are false
3. C
   Statement I is false but statement II is true
4. D
   Statement I is true but statement II is false

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