1
MHT CET 2025 25th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\frac{x^2}{\mathrm{a}^2}+\frac{y^2}{\mathrm{~b}^2}=1$, then $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}$ is

A
$\frac{-b^4}{a}$
B
$\frac{\mathrm{b}^4}{\mathrm{a}^2}$
C
$\frac{-\mathrm{b}^4}{y^3}$
D
$\frac{-b^4}{a^2 \cdot y^3}$
2
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=3 x^3+2 x^2 \mathrm{f}^{\prime}(1)+x \mathrm{f}^{\prime \prime}(2)+\mathrm{f}^{\prime \prime \prime}(3)$ then $\mathrm{f}(x)=$ __________ .

A
$\frac{1}{7}\left(3 x^3-90 x^2+72 x+18\right)$
B
$\frac{1}{7}\left(21 x^3-90 x^2+72 x+126\right)$
C
$3 x^3-90 x^2+72 x+18$
D
$3 x^3-45 x^2+36 x+9$
3
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $x=\sin \theta, y=\sin ^3 \theta$, then $\frac{d^2 y}{d x^2}$ at $\theta=\frac{\pi}{6}$ is

A
$\frac{1}{2}$
B
$\frac{\sqrt{3}}{2}$
C
3
D
6
4
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0
If $x=\mathrm{e}^{\tan ^{-1}\left(\frac{y-x^2}{x^2}\right)}$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=1$ is
A
1
B
0
C
2
D
3
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