1
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $y=\left((x+1)(4 x+1)(9 x+1) \ldots\left(\mathrm{n}^2 x+1\right)\right)^2$, then $\frac{\mathrm{dy}}{\mathrm{d} x}$ at $x=0$ is

A
$\frac{\mathrm{n}(\mathrm{n}+1)(2 \mathrm{n}+1)}{4}$
B
$\frac{\mathrm{n}(\mathrm{n}+1)(2 \mathrm{n}+1)}{6}$
C
$\frac{\mathrm{n}(\mathrm{n}+1)(2 \mathrm{n}+1)}{2}$
D
$\frac{\mathrm{n}(\mathrm{n}+1)(2 \mathrm{n}+1)}{3}$
2
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $y=[(x+1)(2 x+1)(3 x+1) \ldots \ldots \ldots(n x+1)]^4$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=0$ is

A
$\frac{\mathrm{n}(\mathrm{n}+1)}{2}$
B
$4 \mathrm{n}(\mathrm{n}+1)$
C
$\left(\frac{\mathrm{n}(\mathrm{n}+1)}{2}\right)^2$
D
$2 \mathrm{n}(\mathrm{n}+1)$
3
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Derivative of $\sin ^2 x$ with respect to $e^{\cos x}$

A
$2 \sin x \cos ^2 x e^{\cos x}$
B
$\frac{2 \cos x}{\mathrm{e}^{\cos x}}$
C
$\frac{2 \sin x}{\mathrm{e}^{\cos x}}$
D
$\frac{-2 \cos x}{e^{\cos x}}$
4
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $y=\log \left[\mathrm{e}^{5 x}\left(\frac{3 x-4}{x+5}\right)^{\frac{4}{3}}\right]$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

A
$5+\frac{4}{3 x-4}-\frac{4}{3(x+5)}$
B
$5+\frac{4}{3(3 x-4)}-\frac{4}{3(x+5)}$
C
$5 x+\frac{4}{3 x-4}-\frac{4}{3(x+5)}$
D
$5+\frac{12}{3 x-4}-\frac{4}{(x+5)}$
MHT CET Subjects
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