Day 529: MHT-CET Maths

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

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1. A.
   3.0008686
2. B.
   1.99991314
3. C.
   2.0008686
4. D.
   2.9991314

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

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

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1. A.
   15 units
2. B.
   $\sqrt{15} - 2$ units
3. C.
   $\sqrt{15} + 2$ units
4. D.
   $\sqrt{15}$ units

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