1
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $f(1)=1, f^{\prime}(1)=5$, then the derivative of $\mathrm{f}(\mathrm{f}(\mathrm{f}(x)))+(\mathrm{f}(x))^2$ at $x=1$ is

A
125
B
1250
C
135
D
35
2
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $x=\sin \theta, y=\sin ^3 \theta$, then $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}$ at $\theta=\frac{\pi}{2}$ is

A
0
B
2
C
3
D
6
3
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $y=\frac{x^{\frac{2}{3}}-x^{\frac{-1}{3}}}{x^{\frac{2}{3}}+x^{\frac{-1}{3}}}, x \neq 0$, then $(x+1)^2 y_1=$

A
2
B
$-$2
C
$\frac{-1}{3}$
D
3
4
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The derivative of $\sin ^{-1}\left(2 x \sqrt{1-x^2}\right)$ w.r.t. $\sin ^{-1}\left(3 x-4 x^3\right)$ is

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