1
MHT CET 2025 21st April Morning Shift
MCQ (Single Correct Answer)
+2
-0
The function $x^5-5 x^4+5 x^3-10$ has a maximum, when $x$ is equal to
A
0
B
1
C
2
D
3
2
MHT CET 2025 21st April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The function f defined by $\mathrm{f}(x)=(x+2) \mathrm{e}^{-x}$ is

A
decreasing for all $x \in \mathbb{R}$
B
decreasing in $(-\infty,-1)$ and increasing in ( $-1, \infty$ )
C
decreasing in $(-1, \infty)$ and increasing in ( $-\infty,-1$ )
D
increasing for all $x \in \mathbb{R}$
3
MHT CET 2025 21st April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the function $\mathrm{f}(x)=x(x+3) \mathrm{e}^{-\frac{x}{2}}$ satisfies all the conditions of Rolle's theorem in $[-3,0]$, then c is

A
0
B
-1
C
-2
D
-3
4
MHT CET 2025 21st April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $(\mathrm{a}+\mathrm{b} x) \mathrm{e}^{\frac{y}{x}}=x$, then $x^3 \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}$ is equal to

A
$\left(y \frac{\mathrm{~d} y}{\mathrm{~d} x}-x\right)^2$
B
$\left(x \frac{\mathrm{~d} y}{\mathrm{~d} x}-y\right)^2$
C
$\left(x \frac{\mathrm{~d} y}{\mathrm{~d} x}+y\right)^2$
D
$\left(y \frac{\mathrm{~d} y}{\mathrm{~d} x}+x\right)^2$
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