1
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$A(1,-3), B(4,3)$$ are two points on the curve $$y=x-\frac{4}{x}$$. The points on the curve, the tangents at which are parallel to the chord $$A B$$, are

A
$$(1,2),(-1,-2)$$
B
$$(2,0),(-2,0)$$
C
$$(0,2),(1,-2)$$
D
$$(3,2),(-3,1)$$
2
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Water is running in a hemispherical bowl of radius $$180 \mathrm{~cm}$$ 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 $$120 \mathrm{~cm}$$ ? (1 decimeter $$=10 \mathrm{~m}$$)

A
$$16 \pi \mathrm{cm} / \mathrm{sec}$$
B
$$\frac{16}{\pi} \mathrm{cm} / \mathrm{sec}$$
C
$$\frac{1}{16 \pi} \mathrm{cm} / \mathrm{sec}$$
D
$$\frac{\pi}{16} \mathrm{~cm} / \mathrm{sec}$$
3
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If Rolle's theorem holds for the function $$f(x)=x^3+b x^2+a x+5$$ on $$[1,3]$$ with $$c=2+\frac{1}{\sqrt{3}}$$, then the values of $$a$$ and $$b$$ respectively are

A
$$-11,-6$$
B
$$11,6$$
C
$$11,-6$$
D
$$6,11$$
4
MHT CET 2023 13th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\mathrm{f}(x)=x^3+\mathrm{b} x^2+\mathrm{c} x+\mathrm{d}$$ and $$0<\mathrm{b}^2<\mathrm{c}$$, then in $$(-\infty, \infty)$$

A
$$\mathrm{f}(x)$$ has a local maxima.
B
$$\mathrm{f}(x)$$ is strictly increasing function.
C
$$\mathrm{f}(x)$$ is bounded.
D
$$\mathrm{f}(x)$$ is strictly decreasing function.
MHT CET Subjects
EXAM MAP