1
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=\frac{x^2-x}{x^2+2 x}$ then $\frac{\mathrm{d}}{\mathrm{d} x}\left(\mathrm{f}^{-1}(x)\right)$ at $x=2$ is

A
$-3$
B
3
C
$-1$
D
1
2
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $y=A \cos \mathrm{n} x+\mathrm{B} \sin \mathrm{nx}$, then $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}=$

A
$-\mathrm{n}^2 y$
B
$\mathrm{n}^2 y$
C
$\mathrm{n}^2 x$
D
$ \mathrm{n}^2 x^2$
3
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the function $\mathrm{f}(x)=x^3+\mathrm{e}^{\frac{x}{2}}$ and $\mathrm{g}(x)=\mathrm{f}^{-1}(x)$ then the value of $g^{\prime}(1)$ is

A
1
B
0
C
2
D
$\frac{1}{2}$
4
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
$\frac{\mathrm{n}(\mathrm{n}+1)(2 \mathrm{n}+1)}{3}$
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