Build a question paper in 60 seconds.

1. A
   $(-e^{-2}, 2e^{-2})$
2. B
   $(-e^{-2}, -2e^{-2})$
3. C
   $(e^{-2}, 2e^{-2})$
4. D
   $(e^{-2}, -2e^{-2})$

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

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

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1. A
   $\frac{1}{9}$
2. B
   $\frac{2}{9}$
3. C
   $\frac{7}{9}$
4. D
   $\frac{8}{9}$

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1. A
   $\log_3 e$
2. B
   $\log_e 3$
3. C
   $\frac{1}{2}\log_e 3$
4. D
   $2\log_3 e$

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1. A
   $x+2y \geq 50,\; 2x+y \leq 100,\; 2x-y \leq 0,\; x,y \geq 0$
2. B
   $x+2y \leq 50,\; 2x+y \leq 100,\; 2x-y \leq 0,\; x,y \geq 0$
3. C
   $x+2y \geq 50,\; 2x+y \geq 100,\; 2x-y \leq 0,\; x,y \geq 0$
4. D
   $x+2y \leq 50,\; 2x+y \geq 100,\; 2x-y \leq 0,\; x,y \geq 0$

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1. A
   rectangle.
2. B
   square.
3. C
   rhombus.
4. D
   cyclic quadrilateral.

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1. A
   $\frac{1}{100}$
2. B
   $1$
3. C
   $10$
4. D
   $100$

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

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

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1. A
   $\frac{C\vec{A}+\vec{A}\times\vec{B}}{|\vec{A}|^2}$
2. B
   $\frac{C\vec{A}\times\vec{B}}{|\vec{A}|^2}$
3. C
   $\frac{C\vec{A}-\vec{A}\times\vec{B}}{|\vec{A}|^2}$
4. D
   $\frac{C\vec{A}+\vec{B}}{|\vec{A}|^2}$

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1. A
   119
2. B
   107
3. C
   109
4. D
   108

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1. A
   parabola
2. B
   hyperbola
3. C
   circle
4. D
   straight line

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1. A
   $n\pi + (-1)^n\frac{\pi}{3},\; n\in\mathbb{Z}$
2. B
   $n\pi + (-1)^n\frac{\pi}{6},\; n\in\mathbb{Z}$
3. C
   $n\pi \pm (-1)^n\frac{\pi}{4},\; n\in\mathbb{Z}$
4. D
   $n\pi + (-1)^n\frac{2\pi}{3},\; n\in\mathbb{Z}$

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

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1. A
   $2\sqrt{3}$ sq. units
2. B
   $\frac{4}{\sqrt{13}}$ sq. units
3. C
   $\sqrt{13}$ sq. units
4. D
   $\frac{4}{3}$ sq. units

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1. A
   -122
2. B
   -222
3. C
   222
4. D
   122

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

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1. A
   $b^2 = 3a^2+c^2+d^2$
2. B
   $b^2 = a^2+c^2+3d^2$
3. C
   $b^2 = 3a^2+c^2-9d^2$
4. D
   $b^2 = 3a^2+c^2+9d^2$

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1. A
   36
2. B
   18
3. C
   $\frac{27}{4}$
4. D
   9

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1. A
   $\frac{\pi}{2}$
2. B
   $\frac{5\pi}{6}$
3. C
   $\frac{2\pi}{3}$
4. D
   $\frac{3\pi}{4}$

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1. A
   $\sqrt{3}\log(\sqrt{3})$
2. B
   $-\sqrt{3}\log 3$
3. C
   $-\sqrt{3}\log(3)$
4. D
   $\sqrt{3}\log 3$

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1. A
   $f(x)g(x) - f'(x)g'(x)$
2. B
   $f'(x)g(x) - f(x)g'(x)$
3. C
   $f(x)g'(x) - f'(x)g(x)$
4. D
   $f(x)g'(x) + f'(x)g(x)$

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

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1. A
   16
2. B
   40
3. C
   60
4. D
   180

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