Build a question paper in 60 seconds.

1. A
   $\sin\alpha\left(\log(\sin(x-\alpha)\cdot\csc x)\right)+c$
2. B
   $\csc\alpha\left(\log(\sin(x-\alpha)\cdot\csc x)\right)+c$
3. C
   $-\sin\alpha\left(\log(\sin(x-\alpha)\cdot\sin x)\right)+c$
4. D
   $-\csc\alpha\left(\log(\sin(x-\alpha)\cdot\sin x)\right)+c$

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1. A
   $30^\circ$
2. B
   $45^\circ$
3. C
   $60^\circ$
4. D
   $90^\circ$

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1. A
   $\frac{1}{24}$
2. B
   $\frac{1}{16}$
3. C
   $\frac{1}{8}$
4. D
   $\frac{1}{4}$

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

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1. A
   circle
2. B
   pair of straight lines
3. C
   hyperbola
4. D
   ellipse

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1. A
   $30$
2. B
   $\frac{53}{3}$
3. C
   $16$
4. D
   $18$

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1. A
   $104$
2. B
   $100$
3. C
   $102$
4. D
   $103$

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1. A
   $y_3=1$
2. B
   $y_3=-1$
3. C
   $y_3=0$
4. D
   $y\cdot y_3+y_1=0$

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1. A
   $\frac{\tan^{-1}x}{2}e^{\tan^{-1}x}+c$
2. B
   $\tan^{-1}x\cdot e^{\tan^{-1}x}+c$
3. C
   $\frac{\tan^{-1}x}{2}e^{2\tan^{-1}x}+c$
4. D
   $\frac{\tan^{-1}x}{2}e^{2\tan^{-1}x}+c$

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1. A
   $6R=t+2$
2. B
   $R(t+2)=6$
3. C
   $R=6(t+2)$
4. D
   $6R=t$

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1. A
   $\frac{\pi}{10}$
2. B
   $\frac{7\pi}{10}$
3. C
   $\frac{9\pi}{10}$
4. D
   $\frac{3\pi}{10}$

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

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

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1. A
   $5\sqrt{2}$
2. B
   $5$
3. C
   $2\sqrt{5}$
4. D
   $\sqrt{20}$

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1. A
   $\hat{u}=\frac{\hat{a}+\hat{b}}{|\hat{a}+\hat{b}|}$ and $M=(1+\hat{a}\cdot\hat{b})^{1/2}$
2. B
   $\hat{u}=\frac{\hat{a}-\hat{b}}{|\hat{a}-\hat{b}|}$ and $M=(1+\hat{a}\cdot\hat{b})^{1/2}$
3. C
   $\hat{u}=\frac{\hat{a}+\hat{b}}{|\hat{a}+\hat{b}|}$ and $M=(1+2\hat{a}\cdot\hat{b})^{1/2}$
4. D
   $\hat{u}=\frac{\hat{a}-\hat{b}}{|\hat{a}-\hat{b}|}$ and $M=(1+2\hat{a}\cdot\hat{b})^{1/2}$

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