1
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $y=4 x-5$ is a tangent to the curve $y^2=p x^3+q$ at $(2,3)$, then the values of $p$ and $q$ are respectively

A
$-2,7$
B
$7,-2$
C
$2,-7$
D
$-7,-2$
2
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Water is running in a hemispherical bowl of radius 180 cm at the rate of 108 cubic decimeters per minute. How fast the water level is rising when depth of the water level in the bowl is 120 cm ? ( 1 decimeter $=10 \mathrm{~cm}$)

A
$16 \pi \mathrm{~cm} / \mathrm{s}$
B
$\frac{16}{\pi} \mathrm{~cm} / \mathrm{s}$
C
$\frac{1}{16 \pi} \mathrm{~cm} / \mathrm{s}$
D
$\frac{\pi}{16} \mathrm{~cm} / \mathrm{s}$
3
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A point moves along the arc of parabola $y=2 x^2$. Its abscissa increases uniformly at the rate of 2 units $/ \mathrm{sec}$. At the instant, the point is passing through ( 1,2 ), its distance from origin is increasing at the rate of

A
$\frac{36}{\sqrt{5}}$ units/sec.
B
$\frac{18}{\sqrt{5}}$ units $/ \mathrm{sec}$.
C
$\frac{36}{5}$ units/sec.
D
$\frac{18}{5}$ units $/ \mathrm{sec}$.
4
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

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

A
$x+y=3 \mathrm{e}^{-2}$
B
$x-y=3 \mathrm{e}^{-2}$
C
$ x-y=3 \mathrm{e}^2$
D
$x+y=3 \mathrm{e}^2$
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