1
MHT CET 2022 11th August Evening Shift
+2
-0

If $$y=\cos \left(\sin x^2\right)$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ at $$x=\sqrt{\frac{\pi}{2}}$$ is

A
0
B
2
C
$$-$$1
D
$$-$$2
2
MHT CET 2022 11th August Evening Shift
+2
-0

A spherical iron ball of $$10 \mathrm{~cm}$$ radius is coated with a layer of ice of uniform thickness that melts at the rate of $$50 \mathrm{~cm}^3 / \mathrm{min}$$. If the thickness of ice is $$5 \mathrm{~cm}$$, then the rate at which the thickness of ice decreases is

A
$$\frac{-1}{18 \pi} \mathrm{cm} / \mathrm{min}$$
B
$$\frac{2}{9 \pi} \mathrm{cm} / \mathrm{min}$$
C
$$\frac{1}{18 \pi} \mathrm{cm} / \mathrm{min}$$
D
$$\frac{1}{3 \pi} \mathrm{cm} / \mathrm{min}$$
3
MHT CET 2021 24th September Evening Shift
+2
-0

The distance 's' in meters covered by a particle in t seconds is given by $$s=2+27 t-t^3$$. The particle will stop after _________ distance.

A
65 meters
B
80 meters
C
56 meters
D
60 meters
4
MHT CET 2021 24th September Evening Shift
+2
-0

The curve $$y=a x^3+b x^2+c x+5$$ touches $$X$$-axis at $$P(-2,0)$$ and cuts $$Y$$-axis at a point $$Q$$, where its gradient is 3, then

A
$$\mathrm{a}=\frac{1}{2}, \mathrm{~b}=\frac{3}{4}, \mathrm{c}=3$$
B
$$\mathrm{a}=\frac{1}{2}, \mathrm{~b}=\frac{-1}{4}, \mathrm{c}=-3$$
C
$$a=\frac{1}{2}, b=\frac{-3}{4}, c=-3$$
D
$$a=\frac{-1}{2}, b=\frac{-3}{4}, c=3$$
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