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1. A
   $\cos^{-1}\!\left(\frac{17}{35}\right)$
2. B
   $\cos^{-1}\!\left(\frac{17}{31}\right)$
3. C
   $\cos^{-1}\!\left(\frac{19}{35}\right)$
4. D
   $\cos^{-1}\!\left(\frac{19}{31}\right)$

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

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1. A
   fixed radius of 1 unit and variable centres along the X-axis
2. B
   fixed radius of 1 unit and variable centres along the Y-axis
3. C
   variable radii and a fixed centre at (0, 1)
4. D
   variable radii and a fixed centre at (0, −1)

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

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1. A
   425
2. B
   275
3. C
   350
4. D
   225

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

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1. A
   4500
2. B
   3000
3. C
   2500
4. D
   3500

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1. A
   $-\dfrac{5}{9}\log(x+1)+\dfrac{5}{9}\log(x-2)-\dfrac{4}{3}\cdot\dfrac{1}{x-2}+C$
2. B
   $-\dfrac{5}{9}\log(x+1)+\dfrac{5}{9}\log(x-2)-\dfrac{1}{x-2}+C$
3. C
   $\dfrac{1}{9}\log(x+1)+\dfrac{5}{9}\log(x-2)-\dfrac{4}{3}\cdot\dfrac{1}{x-2}+C$
4. D
   $-\dfrac{5}{9}\log(x+1)+\dfrac{1}{9}\log(x-2)-\dfrac{1}{x-2}+C$

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

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1. A
   1.1
2. B
   1.6
3. C
   1.8
4. D
   0.6

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1. A
   −4
2. B
   −7
3. C
   7
4. D
   −3

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

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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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