Day 152: MHT-CET Maths

1. A.
   $-\dfrac{1}{2}\log|e^{2x} + e^x + 1| + \sqrt{3}\tan^{-1}\left(\dfrac{2e^x + 1}{\sqrt{3}}\right) + c$
2. B.
   $-\dfrac{1}{2}\log|e^{2x} + e^x + 1| + \dfrac{\sqrt{3}}{2}\log\left|\dfrac{2e^x + 1 - \sqrt{3}}{2e^x + 1 + \sqrt{3}}\right| + c$
3. C.
   $-\dfrac{1}{2}\log|e^{2x} + e^x + 1| - \sqrt{3}\tan^{-1}\left(\dfrac{2e^x + 1}{\sqrt{3}}\right) + c$
4. D.
   $-\dfrac{1}{2}\log|e^{2x} + e^x + 1| - \dfrac{\sqrt{3}}{2}\log\left|\dfrac{2e^x + 1 - \sqrt{3}}{2e^x + 1 + \sqrt{3}}\right| + c$

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

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1. A.
   $360\ km/hr$
2. B.
   $430\ km/hr$
3. C.
   $600\ km/hr$
4. D.
   $250\ km/hr$

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1. A.
   $8$
2. B.
   $-8$
3. C.
   $\dfrac{1}{8}$
4. D.
   $\dfrac{-1}{8}$

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1. A.
   $18, \dfrac{2}{3}$
2. B.
   $\dfrac{3}{2}, 18$
3. C.
   $\dfrac{2}{3}, 18$
4. D.
   $-\dfrac{2}{3}, 18$

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