Day 531: MHT-CET Maths

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

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

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1. A.
   increasing on $(0,\infty)$.
2. B.
   increasing on $\left(0,\frac{\pi}{e}\right)$, decreasing on $\left(\frac{\pi}{e},\infty\right)$.
3. C.
   decreasing on $(0,\infty)$.
4. D.
   decreasing on $\left(0,\frac{\pi}{e}\right)$, increasing on $\left(\frac{\pi}{e},\infty\right)$.

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

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1. A.
   $e^{\sin^2 x+\cos^3 x}+c$, where c is a constant of integration.
2. B.
   $-e^{-\sin^2 x+\cos^3 x}+c$, where c is a constant of integration.
3. C.
   $e^{-\sin^2 x+\cos^3 x+2}+c$, where c is a constant of integration.
4. D.
   $e^{\sin^2 x+\cos x}+c$, where c is a constant of integration.

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