Day 542: MHT-CET Maths

1. A.
   0
2. B.
   6
3. C.
   12
4. D.
   18

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1. A.
   $x+\alpha$ and $\log|\sin(x+\alpha)|$
2. B.
   $x-\alpha$ and $\log|\sin(x-\alpha)|$
3. C.
   $x-\alpha$ and $\log|\cos(x+\alpha)|$
4. D.
   $x+\alpha$ and $\log|\sin(x-\alpha)|$

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

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

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

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