1
MHT CET 2026 13th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
If $y = x + e^x$, then $\dfrac{d^2 x}{dy^2}$ is equal to
A
$\dfrac{e^x}{(1 + e^x)^2}$
B
$\dfrac{-e^x}{(1 + e^x)^2}$
C
$\dfrac{e^x}{(1 + e^x)^3}$
D
$\dfrac{-e^x}{(1 + e^x)^3}$
2
MHT CET 2026 13th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
Let $f(x) = x - 5$.
If $g(x) = [f(4h(x) + 3)]^2$ and $h(1) = 4, h'(1) = -2$, then $g'(1) =$ .....
A
$-242$
B
$-224$
C
$-112$
D
$-640$
3
MHT CET 2026 13th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
The equation of the normal to the curve $xy + 7 = 0$ is $Ax + By + C = 0$, then
A
$A > 0, B > 0$ or $A < 0, B < 0$
B
$A > 0, B < 0$
C
$A < 0, B > 0$
D
$C = 0$
4
MHT CET 2026 13th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
A wire 40 metre in length is to be cut into two pieces. One piece is formed into a square and the other piece into a circle. The lengths of the two pieces so that the combined area of the square and the circle is minimum, are respectively
A
$\dfrac{160}{\pi + 4}, \dfrac{40\pi}{\pi + 4}$
B
$\dfrac{\pi + 4}{160}, \dfrac{40\pi}{\pi + 4}$
C
$\dfrac{160}{\pi + 4}, \dfrac{\pi + 4}{40\pi}$
D
$30, 10$

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