1
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
In the mean value theorem, $f^{\prime}(c)=\frac{f(b)-f(a)}{b-a}$, if $\mathrm{a}=0, \mathrm{~b}=\frac{1}{2}$ and $\mathrm{f}(x)=x(x-1)(x-2)$, then the value of $c$ is
A
$1-\frac{\sqrt{15}}{6}$
B
$\quad 1-\frac{\sqrt{13}}{6}$
C
$\quad 1-\frac{\sqrt{21}}{6}$
D
$1+\frac{\sqrt{21}}{6}$
2
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The rate of change of the volume of a sphere with respect to its surface area, when its radius is 2 cm , is _________ $\mathrm{cm}^3 / \mathrm{cm}^2$.

A
0.1
B
0.5
C
1
D
2
3
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
$\frac{\pi}{4} \mathrm{~m} / \mathrm{min}$
4
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
$x+y=3 \mathrm{e}^2$
MHT CET Subjects
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