Day 118: MHT-CET Maths

1. A.
   $n = 20$ and $Re(z) = 10$
2. B.
   $n = 20$ and $Re(z) = - 10$
3. C.
   $n = 40$ and $Re(z) = 10$
4. D.
   $n = 40$ and $Re(z) = - 10$

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1. A.
   1
2. B.
   3
3. C.
   $\ \log2$
4. D.
   $\frac{1}{2}$

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1. A.
   $\ x^{2}\frac{{\text{ }d}^{2}y}{\text{ }dx^{2}} + \left( 1 + y^{2} \right) = 0$
2. B.
   $\frac{d^{2}y}{\text{ }dx^{2}} - \frac{dy}{\text{ }dx} + y = 0$
3. C.
   $\frac{d^{2}y}{\text{ }dx^{2}} - 2\frac{\text{ }dy}{\text{ }dx} + 2y = 0$
4. D.
   $x\frac{{\text{ }d}^{2}y}{\text{ }dx^{2}} - 2\frac{\text{ }dy}{\text{ }dx} + 2y = 0$

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

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1. A.
   0
2. B.
   $\frac{\pi}{3}$
3. C.
   $\frac{- \pi}{3}$
4. D.
   $\frac{3}{\pi}$

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