Build a question paper in 60 seconds.

1. A
   only two points
2. B
   only three points
3. C
   four or more points
4. D
   only one point

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

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

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

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

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1. A
   $\frac{1}{24}\log\left|\frac{5+4\sec x}{5-4\sec x}\right|+c$
2. B
   $\frac{1}{40}\log\left|\frac{5+4\sec x}{5-4\sec x}\right|+c$
3. C
   $\frac{1}{24}\log\left|\frac{5-4\sec x}{5+4\sec x}\right|+c$
4. D
   $\frac{1}{40}\log\left|\frac{5-4\sec x}{5+4\sec x}\right|+c$

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1. A
   275
2. B
   510
3. C
   219
4. D
   256

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1. A
   $\frac{m_{0}}{h}(\log 2)$
2. B
   $\frac{m_{0}}{h}(\log 2)$
3. C
   $-\frac{m_{0}}{h}(\log 2)$
4. D
   $-\frac{m_{0}}{h}(\log 2)$

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

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1. A
   If the squares of two numbers are equal, then the numbers are not equal.
2. B
   If the squares of two numbers are not equal, then the numbers are equal.
3. C
   If the squares of two numbers are not equal, then the numbers are not equal.
4. D
   If the squares of two numbers are equal, then the numbers are equal.

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1. A
   a unique solution
2. B
   exactly two solutions
3. C
   no solution
4. D
   infinitely many solutions

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1. A
   $f(x)$ is decreasing in $(-\infty,10]$ and increasing in $[10,\infty)$
2. B
   $f(x)$ is increasing in $(-\infty,10]$ and decreasing in $[10,\infty)$
3. C
   $f(x)$ is increasing throughout real line
4. D
   $f(x)$ is decreasing throughout real line

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

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

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1. A
   2
2. B
   4
3. C
   3
4. D
   no

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1. A
   $\frac{2}{5}\tan^{-1}\!\left(\frac{5\tan(x/2)+4}{3}\right)+c$
2. B
   $\frac{2}{3}\tan^{-1}\!\left(\frac{5\tan(x/2)+4}{3}\right)+c$
3. C
   $\frac{2}{5}\log\!\left|\frac{5\tan(x/2)+7}{5\tan(x/2)+1}\right|+c$
4. D
   $\frac{2}{3}\log\!\left|\frac{5\tan(x/2)+7}{5\tan(x/2)+1}\right|+c$

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1. A
   F, F, F
2. B
   T, T, F
3. C
   T, F, F
4. D
   F, T, T

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

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1. A
   unbounded
2. B
   bounded region, but not a singleton set
3. C
   singleton set
4. D
   null set

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1. A
   $\{0,1,-1\}$
2. B
   $\{0,-1\}$
3. C
   $\left\{0,-1,\frac{-3+i\sqrt{3}}{2},\frac{-3-i\sqrt{3}}{2}\right\}$ where $i=\sqrt{-1}$
4. D
   $\phi$

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1. A
   $\frac{1}{4}$
2. B
   $\frac{3}{28}$
3. C
   $\frac{5}{28}$
4. D
   $\frac{3}{4}$

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1. A
   $\frac{-\hat{i}-3\hat{j}+\hat{k}}{\sqrt{11}}$
2. B
   $\frac{\hat{i}-3\hat{j}+\hat{k}}{\sqrt{11}}$
3. C
   $\frac{\hat{i}+3\hat{j}-\hat{k}}{\sqrt{11}}$
4. D
   $\frac{\hat{i}+3\hat{j}+\hat{k}}{\sqrt{11}}$

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1. A
   $\frac{17}{243}$
2. B
   $\frac{13}{243}$
3. C
   $\frac{11}{243}$
4. D
   $\frac{10}{243}$

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1. A
   $\frac{11}{\sqrt{6}}$ units
2. B
   $\frac{11}{\sqrt{6}}$ units
3. C
   $11$ units
4. D
   $\frac{6}{\sqrt{11}}$ units

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1. A
   4
2. B
   8
3. C
   10
4. D
   12

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