Day 392: MHT-CET Maths

1. A.
   $2xe^{\tan^{- 1}y} = e^{2\tan^{- 1}y} + k$, where k is the constant of integration
2. B.
   $x \cdot e^{\tan^{- 1}y} = e^{\tan^{- 1}y} + k$, where k is the constant of integration
3. C.
   $x \cdot e^{2\tan^{- 1}y} = e^{\tan^{- 1}y} + k$, where k is the constant of integration
4. D.
   $\ x = 2 + k \cdot e^{- \tan^{- 1}y}$, where k is the constant of integration

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1. A.
   $\frac{y\sin x+(1+y)\cos x}{1+2y+\cos x-\sin x}$
2. B.
   $\frac{y\cos x+(1+y)\sin x}{1+2y+\cos x-\sin x}$
3. C.
   $\frac{y\sin x-(1+y)\cos x}{1+2y+\cos x-\sin x}$
4. D.
   $\frac{y\cos x-(1+y)\sin x}{1+2y+\cos x-\sin x}$

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1. A.
   $2\sqrt{x}-\tan^{-1}\sqrt{x}+c$
2. B.
   $2\sqrt{x}-\tan^{-1}\sqrt{x}+c$
3. C.
   $2\sqrt{x}+\tan^{-1}\sqrt{x}+c$
4. D.
   $2\sqrt{x}+\tan^{-1}\sqrt{x}+c$

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1. A.
   $\sqrt{\frac{35}{2}}$
2. B.
   $\frac{\sqrt{35}}{2}$
3. C.
   $7\sqrt{2}$
4. D.
   $\sqrt{35}$

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1. A.
   $\begin{pmatrix} 1 & -\frac{1}{2} \\ 2 & \frac{3}{2} \end{pmatrix}$
2. B.
   $\begin{pmatrix} 1 & \frac{1}{2} \\ -2 & \frac{3}{2} \end{pmatrix}$
3. C.
   $\begin{pmatrix} 1 & -\frac{1}{2} \\ -2 & \frac{3}{2} \end{pmatrix}$
4. D.
   $\begin{pmatrix} 1 & \frac{1}{2} \\ 2 & \frac{3}{2} \end{pmatrix}$

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