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

If the normal to the curve $$y=f(x)$$ at the point $$(3,4)$$ makes an angle $$\left(\frac{3 \pi}{4}\right)^c$$ with positive $$X$$-axis, then $$f^{\prime}(3)$$ is equal to

A
$$-1$$
B
$$\frac{4}{3}$$
C
$$-\frac{3}{4}$$
D
1
2
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
3
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
$$\frac{1}{3 \pi} \mathrm{cm} / \mathrm{min}$$
4
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
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