Build a question paper in 60 seconds.

1. A
   $6\sin(\log 5)$
2. B
   $5\sin(\log 6)$
3. C
   $12\sin(\log 5)$
4. D
   $5\sin(\log 12)$

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1. A
   2
2. B
   7
3. C
   $\sqrt{14}$
4. D
   $\sqrt{14}$

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1. A
   $\frac{1}{\sin(b-a)}\log\left|\frac{\sin(x-a)}{\sin(x-b)}\right| + c$
2. B
   $\log\left|\frac{\sin(x-a)}{\sin(x-b)}\right| + c$
3. C
   $\frac{1}{\sin(b-a)}\log\left|\frac{\sin(x-a)}{\sin(x-b)}\right| + c$
4. D
   $\frac{1}{\sin(b-a)}\log\left|\frac{\sin(x-b)}{\sin(x-a)}\right| + c$

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1. A
   $\frac{1-\cos x}{2y-1}$
2. B
   $\frac{1+\cos x}{2y-1}$
3. C
   $\frac{1-\cos x}{2y+1}$
4. D
   $\frac{1-\sin x}{2y-1}$

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1. A
   4 units
2. B
   5 units
3. C
   6 units
4. D
   7 units

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1. A
   10
2. B
   12
3. C
   9
4. D
   6

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1. A
   $5+\sqrt{6}$
2. B
   $5-1$
3. C
   $\sqrt{6}+1$
4. D
   $5+1$

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1. A
   $\begin{pmatrix}-\frac{1}{2} & 0\\-\frac{3}{2} & \frac{1}{2}\end{pmatrix}$
2. B
   $\begin{pmatrix}\frac{1}{2} & 0\\\frac{3}{2} & -\frac{1}{2}\end{pmatrix}$
3. C
   $\begin{pmatrix}\frac{1}{2} & 0\\-\frac{3}{2} & \frac{1}{2}\end{pmatrix}$
4. D
   $\begin{pmatrix}\frac{1}{2} & 0\\\frac{3}{2} & \frac{1}{2}\end{pmatrix}$

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

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1. A
   $-2\hat{i}+7\hat{j}+13\hat{k}$
2. B
   $2\hat{i}-7\hat{j}+13\hat{k}$
3. C
   $-\hat{i}-4\hat{j}+7\hat{k}$
4. D
   $\hat{i}-4\hat{j}+7\hat{k}$

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1. A
   $\sin^2\alpha$
2. B
   $3\sin^2\alpha$
3. C
   $9\sin^2\alpha$
4. D
   $49\sin^2\alpha$

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

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

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

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

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

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1. A
   $p$
2. B
   $p \to (p \vee \sim q)$
3. C
   $p \wedge (\sim p \wedge q)$
4. D
   $(p \vee \sim q) \to p$

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1. A
   $e^x\frac{x}{x+4} + c$
2. B
   $e^x\frac{4}{x+4} + c$
3. C
   $\frac{e^x x}{(x+4)^2} + c$
4. D
   $\frac{e^x 4}{(x+4)^2} + c$

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1. A
   15
2. B
   -15
3. C
   12
4. D
   -12

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1. A
   $\frac{n+1}{6}$
2. B
   $\frac{2n+1}{6}$
3. C
   $\frac{n+1}{3}$
4. D
   $\frac{2n+1}{3}$

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1. A
   $\left(\frac{1}{3},-\frac{7}{3}\right)$
2. B
   $\left(-\frac{1}{3},-\frac{7}{3}\right)$
3. C
   $\left(-\frac{1}{3},\frac{7}{3}\right)$
4. D
   $\left(\frac{1}{3},\frac{7}{3}\right)$

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1. A
   -5
2. B
   5
3. C
   9
4. D
   -9

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1. A
   $\dfrac{7}{5}\!\left(\dfrac{9}{10}\right)^4$
2. B
   $\dfrac{7}{5}\!\left(\dfrac{9}{10}\right)^5$
3. C
   $\dfrac{6}{5}\!\left(\dfrac{9}{10}\right)^4$
4. D
   $\dfrac{6}{5}\!\left(\dfrac{9}{10}\right)^5$

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1. A
   $2x+3y\geq6,\,-x+2y\geq2,\,3x+6y\leq18,\,x-3y\geq3,\,x\geq0,y\geq0$
2. B
   $2x+3y\geq6,\,-x+2y\leq2,\,x-3y\leq3,\,x+2y\geq18,\,x\geq0,y\geq0$
3. C
   $2x+3y\leq6,\,-x+2y\geq2,\,3x+6y\leq18,\,x-3y\leq3,\,x\geq0,y\geq0$
4. D
   $2x+3y\geq6,\,3x+6y\leq18,\,x-3y\leq3,\,-x+2y\leq2,\,x\geq0,y\geq0$

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1. A
   $20\sqrt{2}\,\text{cm}^2/\text{sec}$
2. B
   $10\sqrt{2}\,\text{cm}^2/\text{sec}$
3. C
   $\frac{1}{10}\sqrt{2}\,\text{cm}^2/\text{sec}$
4. D
   $\frac{1}{0}\sqrt{2}\,\text{cm}^2/\text{sec}$

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