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1
MHT CET 2026 15th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
If $y = \left(\dfrac{ax+b}{cx+d}\right)$, then $2\dfrac{dy}{dx} \cdot \dfrac{d^3 y}{dx^3}$ is equal to
A
$\left(\dfrac{d^2 y}{dx^2}\right)^2$
B
$3\dfrac{d^2 y}{dx^2}$
C
$3\left(\dfrac{d^2 y}{dx^2}\right)^2$
D
$3\dfrac{d^2 x}{dy^2}$
2
MHT CET 2026 15th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
Let $f(x) = 3x^3 + 4e^{\frac{x}{2}}$ and $g(x) = f^{-1}(x)$. Then the value of $g'(4)$ is equal to...
A
$4$
B
$2$
C
$1$
D
$\dfrac{1}{2}$
3
MHT CET 2025 5th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Derivative of

$y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\ldots \ldots \ldots \ldots \ldots \ldots \infty}}}$ is

A

$\frac{\sin x}{1-2 y}$

B

$\frac{\cos x}{1-2 y}$

C

$\frac{\sin x}{1+2 y}$

D

$\frac{\cos x}{2 y-1}$

4
MHT CET 2025 5th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $x \cdot \log _e\left(\log _e x\right)-x^2+y^2=4(y>0)$, then $\frac{d y}{d x}$ at $x=\mathrm{e}$ is

A
$\frac{\mathrm{e}}{\sqrt{4+\mathrm{e}^2}}$
B
$\quad \frac{2 \mathrm{e}-1}{2 \sqrt{4+\mathrm{e}^2}}$
C
$\frac{1+2 e}{\sqrt{4+e^2}}$
D
$\quad \frac{1+2 \mathrm{e}}{2 \sqrt{4+\mathrm{e}^2}}$
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