1. A
   $\frac{1}{8}$
2. B
   $\frac{1}{27}$
3. C
   $\frac{3}{4}$
4. D
   $\frac{3}{8}$

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1. A
   0
2. B
   $- \frac{RT}{2(\gamma - 1)}$
3. C
   $RT\left[ \ln 2 - \frac{1}{2(\gamma - 1)} \right]$
4. D
   $RT\ln 2$

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1. A
   $( -5, -4) \cup (4, \infty)$
2. B
   $( -5, \infty)$
3. C
   $( -\infty, -5) \cup (4, \infty)$
4. D
   $( -\infty, -5) \cup ( -4, \infty)$

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1. A
   lightly doped and have wide depletion layer.
2. B
   heavily doped andhave narrow depletion layer.
3. C
   heavily doped and have wide depletion layer.
4. D
   lightly doped and have narrow depletion layer.

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1. A
   $n = 2$ to $n = 1$
2. B
   $n = 4$ to $n = 3$
3. C
   $n = 5$ to $n = 4$
4. D
   $n = 3$ to $n = 2$

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1. A
   $10^{- 2}\text{ }nm$
2. B
   $10^{- 3}\text{ }nm$
3. C
   $10^{- 4}\text{ }nm$
4. D
   $10^{- 1}\text{ }nm$

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1. A
   suffer change in momentum when impinge on the walls of container.
2. B
   continuously stick to the walls of container.
3. C
   continuously lose their energy till it reaches wall.
4. D
   are attracted by the walls of container.

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1. A
   $\frac{10}{11}a$
2. B
   $\frac{2}{3}a$
3. C
   $\frac{1}{6}a$
4. D
   $\frac{5}{6}a$

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

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1. A
   elliptical
2. B
   parabolic
3. C
   straight line
4. D
   circular

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

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

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1. A
   the fringes will become brighter.
2. B
   consecutive fringe lineswill come closer.
3. C
   the central bright fringe will become a dark fringe.
4. D
   the intensity of minima will increase.

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1. A
   $49\text{ }N$
2. B
   $49.83\text{ }N$
3. C
   $49.17\text{ }N$
4. D
   $48.83\text{ }N$

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1. A
   $1.33\%$
2. B
   $1.30\%$
3. C
   $1.13\%$
4. D
   $1.03\%$

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

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1. A
   $9\text{ }A$
2. B
   $3.0\text{ }A$
3. C
   $2.25\text{ }A$
4. D
   $3.37\text{ }A$

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

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1. A
   $\left( \frac{q^{2}}{2\pi\varepsilon_{0}{md}^{3}} \right)^{\frac{1}{2}}$
2. B
   $\left( \frac{\pi\varepsilon_{0}md^{3}}{2q^{2}} \right)^{\frac{1}{2}}$
3. C
   $\left( \frac{2\pi\varepsilon_{0}md^{3}}{q^{2}} \right)^{\frac{1}{2}}$
4. D
   $\left( \frac{2q^{2}}{\pi\varepsilon_{0}md^{3}} \right)^{\frac{1}{2}}$

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1. A
   decrease in size and changes orientation.
2. B
   may increase or decrease in size and change its orientation.
3. C
   increase in size but no change in orientation.
4. D
   have no relation with external magnetic field.

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1. A
   $y = Ae^{- x^{2}}(vt + \theta)$
2. B
   $\ y = Asin(15x - 2t)$
3. C
   $\ y = Ae^{x}\cos(\omega t - \theta)$
4. D
   $\ y = Asinxcos\omega t$

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1. A
   $\left( \frac{2v_{0}}{3\alpha} \right)^{\frac{1}{3}}$
2. B
   $\left( \frac{3v_{0}^{2}}{2\alpha} \right)^{\frac{1}{2}}$
3. C
   $\left( \frac{3{mv}_{0}^{2}}{2\alpha} \right)^{\frac{1}{3}}$
4. D
   $\left( \frac{2v_{0}^{2}}{3\alpha} \right)^{\frac{1}{2}}$

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1. A
   (iv) $<$ (i) $<$ (iii) $<$ (ii)
2. B
   (iv) $<$ (i) $<$ (ii) $<$ (iii)
3. C
   (i) $<$ (ii) $<$ (iii) $<$ (iv)
4. D
   (iv) $<$ (iii) $<$ (ii) $<$ (i)

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

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

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