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

Water is being poured at the rate of $36 \mathrm{~m}^3 / \mathrm{min}$ into a cylindrical vessel, whose circular base is of radius 3 meters. Then the water level in the cylinder is rising at the rate of

A
$4 \pi \mathrm{~m} / \mathrm{min}$
B
$\frac{4}{\pi} \mathrm{~m} / \mathrm{min}$
C
$\frac{1}{4 \pi} \mathrm{~m} / \mathrm{min}$
D
$\frac{\pi}{4} \mathrm{~m} / \mathrm{min}$
2
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the normal to the curve $y=x \log x$ parallel to $2 x-2 y+3=0$ is

A
$x+y=3 \mathrm{e}^{-2}$
B
$x-y=3 \mathrm{e}^{-2}$
C
$x-y=3 \mathrm{e}^2$
D
$x+y=3 \mathrm{e}^2$
3
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha \log |x|+\beta x^2+x$, then

A
$\alpha=-6, \beta=\frac{1}{2}$
B
$\alpha=-6, \beta=-\frac{1}{2}$
C
$\alpha=2, \beta=-\frac{1}{2}$
D
$\alpha=2, \beta=\frac{1}{2}$
4
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(1)=1, \mathrm{f}^{\prime}(1)=3$, then the derivative of $\mathrm{f}(\mathrm{f}(\mathrm{f}(x)))+(\mathrm{f}(x))^2$ at $x=1$ is

A
12
B
9
C
15
D
33
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