Build a question paper in 60 seconds.

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

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1. A
   $20\sqrt{2}$
2. B
   $\frac{10\sqrt{2}}{3}$
3. C
   $\frac{20\sqrt{2}}{3}$
4. D
   $10\sqrt{2}$

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

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1. A
   16
2. B
   8
3. C
   2
4. D
   4

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1. A
   $8x + y - 58 = 0$
2. B
   $8x - 2y - 52 = 0$
3. C
   $8x - y - 54 = 0$
4. D
   $8x + 2y - 60 = 0$

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

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1. A
   $x + y = 3e^{-2}$
2. B
   $x - y = 3e^{-2}$
3. C
   $x - y = 3e^{2}$
4. D
   $x + y = 3e^{2}$

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1. A
   $\tan^{-1}x \cdot e^{\tan^{-1}x} + c$
2. B
   $\left(\tan^{-1}x\right)^2 e^{\tan^{-1}x} + c$
3. C
   $2\tan^{-1}x \cdot e^{\tan^{-1}x} + c$
4. D
   $2\left(\tan^{-1}x\right)^2 e^{\tan^{-1}x} + c$

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1. A
   $8x + 14y + 13z - 37 = 0$
2. B
   $8x - 14y - 13z - 34 = 0$
3. C
   $8x - 14y - 13z + 37 = 0$
4. D
   $8x + 14y + 13z + 37 = 0$

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

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1. A
   $-\frac{\pi}{4}$
2. B
   $\frac{4\pi}{3}$
3. C
   $\frac{\pi}{12}$
4. D
   $\frac{7\pi}{12}$

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1. A
   $\tan x = (c + \sec x)y$, where c is constant of integration.
2. B
   $\sec y = (c + \tan y)x$, where c is constant of integration.
3. C
   $\sec x = (c + \tan x)y$, where c is constant of integration.
4. D
   $\cos y = (c + \tan y)$, where c is constant of integration.

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

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1. A
   $\frac{8}{35}$
2. B
   $\frac{18}{35}$
3. C
   $\frac{26}{35}$
4. D
   $\frac{34}{35}$

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1. A
   2
2. B
   5
3. C
   10
4. D
   4

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1. A
   $\frac{x^2}{2} + 3x - \log x + c$
2. B
   $\frac{x^2}{2} + 3x + 2\log x + c$
3. C
   $\frac{x^2}{2} - 3x + 2\log x + c$
4. D
   $\frac{x^2}{2} - 3x - \log x + c$

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1. A
   0.2
2. B
   1.2
3. C
   0.8
4. D
   2.5

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1. A
   216
2. B
   240
3. C
   96
4. D
   120

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1. A
   equivalent to $p \leftrightarrow q$
2. B
   a fallacy
3. C
   a tautology
4. D
   equivalent to $\sim p \leftrightarrow q$

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1. A
   $\alpha = -6, \beta = \frac{1}{2}$
2. B
   $\alpha = -6, \beta = -\frac{1}{2}$
3. C
   $\alpha = 2, \beta = -\frac{1}{2}$
4. D
   $\alpha = 2, \beta = \frac{1}{2}$

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1. A
   The terms of $S$ form an arithmetic progression with common difference 14.
2. B
   The terms of $S$ form an arithmetic progression with common difference 6.
3. C
   The terms of $S$ form a geometric progression with common ratio $\frac{10}{7}$.
4. D
   The terms of $S$ form a geometric progression with common ratio $\frac{11}{4}$.

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1. A
   One
2. B
   Two
3. C
   Three
4. D
   More than three

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1. A
   $3$
2. B
   $6$
3. C
   $9$
4. D
   $12$

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1. A
   $0$
2. B
   $1$
3. C
   $4$
4. D
   $5$

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

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