Day 124: MHT-CET Maths

1. A.
   $\tan^{- 1}\left( \frac{42}{24} \right)$
2. B.
   $2\tan^{- 1}\left( \frac{42}{24} \right)$
3. C.
   $\tan^{- 1}\left( \frac{24}{41} \right)$
4. D.
   $\tan^{- 1}\left( \frac{41}{12} \right)$

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1. A.
   10
2. B.
   -10
3. C.
   9
4. D.
   -9

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1. A.
   $\frac{3}{5}(\pi - 2)$
2. B.
   $\frac{15}{2}(\pi - 2)$
3. C.
   $\frac{3}{10}(\pi - 2)$
4. D.
   $\frac{15}{4}(\pi - 2)$

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1. A.
   $\frac{(2 + x)^{2}}{2}\log\left( \frac{2 + x}{\sqrt{e}} \right) + c$, where c is the constant of integration
2. B.
   $\frac{(2 + x)^{2}}{2}\log\left( \frac{2 + x}{e} \right) + c$, where c is the constant of integration
3. C.
   $\ \frac{2 + x}{2}\log\left( \frac{2 + x}{\sqrt{e}} \right) + c$, where c is the constant of integration
4. D.
   $\frac{2 + x}{2}\log(2 + x)\sqrt{e} + c$, where c is the constant of integration

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1. A.
   $\frac{\pi}{4},\frac{5\pi}{12},\frac{\pi}{2},\frac{2\pi}{3},\frac{3\pi}{4},\frac{8\pi}{9}$
2. B.
   $\frac{2\pi}{9},\frac{\pi}{4},\frac{\pi}{2},\frac{2\pi}{3},\frac{3\pi}{4},\frac{35\pi}{36}$
3. C.
   $\frac{2\pi}{9},\frac{\pi}{4},\frac{\pi}{2},\frac{2\pi}{3},\frac{3\pi}{4},\frac{8\pi}{10}$
4. D.
   $\frac{2\pi}{9},\frac{\pi}{4},\frac{4\pi}{9},\frac{\pi}{2},\frac{3\pi}{4},\frac{8\pi}{9}$

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