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1. A
   0
2. B
   6
3. C
   8
4. D
   1

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1. A
   $\frac{3}{2}\tan\frac{3\theta}{2}$
2. B
   $\frac{3}{2}\sec\frac{3\theta}{2}\tan\frac{3\theta}{2}$
3. C
   $\frac{3}{2}\sec^{2}\frac{3\theta}{2}$
4. D
   $\sec^{2}\frac{3\theta}{2}$

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

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1. A
   36 sq. units
2. B
   16 sq. units
3. C
   4 sq. units
4. D
   49 sq. units

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1. A
   30
2. B
   12.5
3. C
   25
4. D
   10

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1. A
   0.1
2. B
   0.5
3. C
   -0.5
4. D
   1

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1. A
   $-\frac{16}{13}$
2. B
   $\frac{13}{10}$
3. C
   $-\frac{13}{16}$
4. D
   $\frac{13}{16}$

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1. A
   0
2. B
   $\frac{1}{32}$
3. C
   $\frac{1}{8}$
4. D
   $\frac{1}{16}$

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1. A
   $\frac{4}{3}$ m/sec
2. B
   $\frac{2}{3}$ m/sec
3. C
   $\frac{5}{3}$ m/sec
4. D
   $\frac{8}{3}$ m/sec

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1. A
   $\left[-\frac{5}{4},-1\right]$
2. B
   $\left[-\frac{3}{2},-\frac{5}{4}\right]$
3. C
   $\left[-\frac{1}{2},-\frac{1}{4}\right]$
4. D
   $\left[-1,-\frac{1}{2}\right]$

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1. A
   $2x-8y+1=0$
2. B
   $8x-2y+1=0$
3. C
   $8x+2y+1=0$
4. D
   $2x-8y-1=0$

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1. A
   15
2. B
   -7
3. C
   7
4. D
   -5

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1. A
   9.00898
2. B
   9.0989
3. C
   9.0898
4. D
   9.00989

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1. A
   (3,-2)
2. B
   (-2,3)
3. C
   (-3,2)
4. D
   (2,-3)

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1. A
   $\vec{u}\cdot(\vec{v}\times\vec{w})$
2. B
   $\vec{u}\cdot(\vec{w}\times\vec{v})$
3. C
   $3\vec{u}\cdot(\vec{v}\times\vec{w})$
4. D
   $0$

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1. A
   4
2. B
   2.5
3. C
   5
4. D
   1

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1. A
   $\frac{d^{2}y}{dx^{2}}+2\frac{dy}{dx}-2y=0$
2. B
   $\frac{d^{2}y}{dx^{2}}-2\frac{dy}{dx}+y=0$
3. C
   $\frac{d^{2}y}{dx^{2}}-2\frac{dy}{dx}-2e^{x}+y=0$
4. D
   $\frac{d^{2}y}{dx^{2}}+2\frac{dy}{dx}-e^{x}+2y=0$

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1. A
   $a=3, b=4$
2. B
   $a=0, b=7$
3. C
   $a=5, b=2$
4. D
   $a=1, b=6$

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1. A
   0
2. B
   1
3. C
   2
4. D
   3

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1. A
   $\pi$ with direction of field.
2. B
   $\frac{\pi}{2}$ with direction of field.
3. C
   $\frac{3\pi}{2}$ with direction of field.
4. D
   zero with direction of field.

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

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1. A
   the work function of the metal.
2. B
   the Planck's constant.
3. C
   the maximum kinetic energy of the ejected electrons.
4. D
   the threshold frequency for photo ejection from the metal.

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1. A
   red colour
2. B
   yellow colour
3. C
   green colour
4. D
   blue colour

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1. A
   $5\times10^5\ \text{Nm}^{-2}$
2. B
   $10^6\ \text{Nm}^{-2}$
3. C
   $0.5\times10^5\ \text{Nm}^{-2}$
4. D
   $5\times10^6\ \text{Nm}^{-2}$

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

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