Build a question paper in 60 seconds.

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

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

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1. A
   (6,5,2)
2. B
   (4,3,2)
3. C
   (6,5,-2)
4. D
   (3,4,-2)

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1. A
   5 m, 5 m, 10 m
2. B
   10 m, 10 m, 5 m
3. C
   2 m, 2 m, 8 m
4. D
   15 m, 15 m, 5 m

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1. A
   $-\sqrt[3]{2}$
2. B
   $\sqrt[3]{2}$
3. C
   $-\sqrt[3]{2}$
4. D
   $\sqrt[3]{2}$

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1. A
   $\sqrt{2}\log\left|\tan\!\left(\frac{x}{2}+\frac{\pi}{4}\right)\right|+c$
2. B
   $\frac{1}{\sqrt{2}}\log\left|\tan\!\left(\frac{x}{2}+\frac{\pi}{8}\right)\right|+c$
3. C
   $\frac{1}{\sqrt{2}}\log\left|\frac{\tan(x/2)-(\sqrt{2}+1)}{\tan(x/2)+(\sqrt{2}-1)}\right|+c$
4. D
   $-\frac{1}{\sqrt{2}}\log\left|\frac{\tan(x/2)-(\sqrt{2}+1)}{\tan(x/2)+(\sqrt{2}-1)}\right|+c$

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

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

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

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1. A
   $49\pi$ sq. units
2. B
   $\frac{49\pi}{2}$ sq. units
3. C
   $\frac{49\pi}{4}$ sq. units
4. D
   $98\pi$ sq. units

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

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1. A
   3
2. B
   4
3. C
   7
4. D
   8

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

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1. A
   $x\log2+\log2x$
2. B
   $x\log2-\log2x$
3. C
   $x\log2x$
4. D
   $\log2x$

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1. A
   $(1+\cos x)(1+\sin y)=c$
2. B
   $1+\sin x+\cos y=c$
3. C
   $(1+\sin x)(1+\cos y)=c$
4. D
   $1+\sin x\cdot\cos y=c$

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

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1. A
   $\alpha>0,b>0$
2. B
   $\alpha>0,b<0$
3. C
   $\alpha<0,b<0$
4. D
   $\alpha=0,b=0$

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1. A
   12 m/sec
2. B
   15 m/sec
3. C
   18 m/sec
4. D
   20 m/sec

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

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1. A
   25
2. B
   27
3. C
   33
4. D
   5

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1. A
   6
2. B
   $\frac{5}{2}$
3. C
   $\frac{9}{4}$
4. D
   $\frac{17}{2}$

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1. A
   300
2. B
   320
3. C
   321
4. D
   322

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1. A
   (1,-2)
2. B
   (0,-4)
3. C
   (2,0)
4. D
   (3,2)

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1. A
   variable radii and fixed centre at (0,1).
2. B
   variable radii and fixed centre at (0,-1).
3. C
   fixed radius 1 and variable centre along Y-axis.
4. D
   fixed radius 1 and variable centre along X-axis.

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

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