Build a question paper in 60 seconds.

1. A
   side of square bottom = 40 cm, height = 10 cm.
2. B
   side of square bottom = 20 cm, height = 10 cm.
3. C
   side of square bottom = 10 cm, height = 40 cm.
4. D
   side of square bottom = 5 cm, height = 160 cm.

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

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

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1. A
   $\frac{17}{3}$ sq. units
2. B
   15 sq. units
3. C
   $\frac{19}{3}$ sq. units
4. D
   9 sq. units

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1. A
   750
2. B
   1500
3. C
   2255
4. D
   2250

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

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1. A
   $x^2+y^2+4x+3y+22=0$
2. B
   $x^2+y^2-4x+3y-22=0$
3. C
   $x^2+y^2-4x-3y-22=0$
4. D
   $x^2+y^2+4x-3y+22=0$

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1. A
   $\left\{\frac{\pi}{6}, \frac{7\pi}{6}, \frac{3\pi}{2}\right\}$
2. B
   $\left\{\frac{\pi}{6}, \frac{5\pi}{6}\right\}$
3. C
   $\left\{\frac{\pi}{6}, \frac{5\pi}{6}, \frac{3\pi}{2}\right\}$
4. D
   $\left\{\frac{5\pi}{6}, \frac{11\pi}{6}, \frac{3\pi}{2}\right\}$

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1. A
   $an^2+2hmn+bm^2=0$
2. B
   $am^2+2hmn+bn^2=0$
3. C
   $am^2-2hmn+bn^2=0$
4. D
   $an^2-2hmn+bm^2=0$

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1. A
   4
2. B
   12
3. C
   5
4. D
   11

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

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

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1. A
   $-1$
2. B
   5
3. C
   3
4. D
   13

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1. A
   $1 < x < 2$
2. B
   $x < 1$ or $x > 2$
3. C
   $x < -1$ or $x > -2$
4. D
   $-2 < x < -1$

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

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

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

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1. A
   X-axis.
2. B
   circle with centre $(1,0)$ and radius 1 unit.
3. C
   circle with centre $(-1,0)$ and radius 1 unit.
4. D
   Y-axis.

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

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

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1. A
   collinear and Q lies between P and R.
2. B
   collinear and R lies between P and Q.
3. C
   collinear and P lies between Q and R.
4. D
   non-collinear.

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1. A
   $135^\circ$
2. B
   $150^\circ$
3. C
   $165^\circ$
4. D
   $180^\circ$

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

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1. A
   $\vec{r}\cdot(\hat{i}-\hat{k})=2$
2. B
   $\vec{r}\cdot(\hat{i}+\hat{k})+2=0$
3. C
   $\vec{r}\cdot(\hat{i}+\hat{k})=2$
4. D
   $\vec{r}\cdot(\hat{i}-\hat{k})+2=0$

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

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