Day 535: JEE Mains Maths

1. A.
   $3\log_{e}4$
2. B.
   $6\log_{e}4$
3. C.
   $4\log_{e}3$
4. D.
   $2\log_{e}3$

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

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1. A.
   $\frac{1}{2}\log_{e}\left| \frac{\tan\left( \frac{x}{2} + \frac{\pi}{12} \right)}{\tan\left( \frac{x}{2} + \frac{\pi}{6} \right)} \right| + C$
2. B.
   $\frac{1}{2}\log_{e}\left| \frac{\tan\left( \frac{x}{2} + \frac{\pi}{6} \right)}{\tan\left( \frac{x}{2} + \frac{\pi}{3} \right)} \right| + C$
3. C.
   $\log_{e}\left| \frac{\tan\left( \frac{x}{2} + \frac{\pi}{6} \right)}{\tan\left( \frac{x}{2} + \frac{\pi}{12} \right)} \right| + C$
4. D.
   $\frac{1}{2}\log_{e}\left| \frac{\tan\left( \frac{x}{2} - \frac{\pi}{12} \right)}{\tan\left( \frac{x}{2} - \frac{\pi}{6} \right)} \right| + C$

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1. A.
   $n^{2}$
2. B.
   $\frac{n(n + 1)}{2}$
3. C.
   $n$
4. D.
   $n^{2} + n$

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1. A.
   16
2. B.
   32
3. C.
   -16
4. D.
   0

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