Day 41: MHT-CET Maths

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

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1. A.
   $\cos^{-1}\left(\dfrac{8}{5\sqrt{5}}\right)$
2. B.
   $\cos^{-1}\left(\dfrac{5}{8\sqrt{5}}\right)$
3. C.
   $\sin^{-1}\left(\dfrac{8}{5\sqrt{5}}\right)$
4. D.
   $\dfrac{\pi}{4}$

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1. A.
   $\dfrac{10}{\sqrt{29}}$
2. B.
   $\dfrac{19}{2\sqrt{29}}$
3. C.
   $\dfrac{5}{\sqrt{41}}$
4. D.
   $\dfrac{10}{\sqrt{41}}$

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1. A.
   $\begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}$
2. B.
   $\begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$
3. C.
   $\begin{bmatrix} \sin\theta & -\cos\theta \\ \cos\theta & \sin\theta \end{bmatrix}$
4. D.
   $\begin{bmatrix} \cos\theta & \sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$

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1. A.
   $x^2 - xy - x + 4y - 12 = 0$
2. B.
   $xy - y^2 - 4x + 7y - 12 = 0$
3. C.
   $x^2 + 2xy - y^2 + 7 = 0$
4. D.
   $xy - 2y^2 + 3x + 2y + 17 = 0$

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