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1. A
   $\frac{4}{169}$
2. B
   $\frac{1}{13}$
3. C
   $\frac{1}{169}$
4. D
   $\frac{2}{13}$

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1. A
   $\left(4, \frac{3\pi}{4}\right)$
2. B
   $\left(4, \frac{5\pi}{6}\right)$
3. C
   $\left(4, \frac{2\pi}{3}\right)$
4. D
   $\left(4, \frac{11\pi}{12}\right)$

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1. A
   $\frac{5}{4}$
2. B
   $\frac{5}{3}$
3. C
   $\frac{34}{3}$
4. D
   $\frac{41}{4}$

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1. A
   $\begin{pmatrix} 60 & 0 & 0 \\ 0 & 60 & 0 \\ 0 & 0 & 60 \end{pmatrix}$
2. B
   $\begin{pmatrix} 108 & 0 & 0 \\ 0 & 108 & 0 \\ 0 & 0 & 108 \end{pmatrix}$
3. C
   $\begin{pmatrix} 20 & 0 & 0 \\ 0 & 20 & 0 \\ 0 & 0 & 20 \end{pmatrix}$
4. D
   $\begin{pmatrix} 68 & 0 & 0 \\ 0 & 68 & 0 \\ 0 & 0 & 68 \end{pmatrix}$

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1. A
   $my^2$
2. B
   $m^2 y$
3. C
   $m^2 y^2$
4. D
   $\frac{my^2}{2}$

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

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1. A
   $3x + y - 11 = 0,\ x + 3y + 9 = 0$
2. B
   $3x - y - 7 = 0,\ x + 3y - 9 = 0$
3. C
   $3x + y - 11 = 0,\ x + 3y - 9 = 0$
4. D
   $x + 2y - 7 = 0,\ 2x - y - 4 = 0$

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1. A
   $\left[\frac{3}{2}, 5\right)$
2. B
   $\left[\frac{7}{2}, 5\right)$
3. C
   $\left[\frac{9}{2}, 5\right)$
4. D
   $\left[\frac{11}{2}, 5\right)$

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1. A
   $\frac{x-1}{-3} = \frac{y-2}{5} = \frac{z-3}{4}$
2. B
   $\frac{x-1}{3} = \frac{y-2}{1} = \frac{z-3}{1}$
3. C
   $\frac{x-1}{1} = \frac{y-2}{-1} = \frac{z-3}{1}$
4. D
   $\frac{x-1}{-3} = \frac{y-2}{-5} = \frac{z-3}{4}$

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1. A
   $x^2+y^2-2x+2y-47=0$
2. B
   $x^2+y^2-2x+2y+51=0$
3. C
   $x^2+y^2+2x-2y-51=0$
4. D
   $x^2+y^2+2x+2y+47=0$

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1. A
   $\frac{-1}{18\pi}$ cm/min
2. B
   $\frac{2}{9\pi}$ cm/min
3. C
   $\frac{1}{18\pi}$ cm/min
4. D
   $\frac{1}{3\pi}$ cm/min

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1. A
   $x + \sin x + \sin 2x + C$
2. B
   $x + \sin x + \sin 2x - C$
3. C
   $x + 2\sin x + 2\sin 2x + C$
4. D
   None of these

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1. A
   $3y + 4z = 13$
2. B
   $y - 4z = -1$
3. C
   $2y + 4z = 19$
4. D
   $y + 4z = 7$

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1. A
   $\frac{N^{2}A^{2}B^{2}\omega^{2}}{2R}$
2. B
   $\frac{BNA\omega}{R}$
3. C
   $\frac{BNA\omega}{2R}$
4. D
   $\frac{N^{2}A^{2}B^{2}\omega^{2}}{R}$

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

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

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1. A
   $\frac{4E}{9}$
2. B
   $\frac{4E}{3}$
3. C
   $\frac{16E}{9}$
4. D
   $\frac{16E}{3}$

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1. A
   capacitance A has high capacity.
2. B
   capacitance B has high capacity.
3. C
   both have same capacity.
4. D
   capacity of A = 2 times capacity of B.

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1. A
   $\sqrt{2gl(1-\cos\theta)}$
2. B
   $\sqrt{2gl(1+\sin\theta)}$
3. C
   $\sqrt{2gl(1-\sin\theta)}$
4. D
   $\sqrt{2gl(1+\cos\theta)}$

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1. A
   maximum potential energy.
2. B
   minimum potential energy.
3. C
   maximum kinetic energy.
4. D
   minimum kinetic energy.

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1. A
   -6.67
2. B
   -1.5
3. C
   +6.67
4. D
   +1.5

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

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1. A
   1
2. B
   2
3. C
   5
4. D
   0.5

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1. A
   $100\,\Omega$
2. B
   $50\,\Omega$
3. C
   $40\,\Omega$
4. D
   $10\,\Omega$

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1. A
   $\frac{1}{6}$ s
2. B
   $\frac{1}{24}$ s
3. C
   $\frac{1}{18}$ s
4. D
   $\frac{1}{12}$ s

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