1
MHT CET 2021 24th September Morning Shift
+2
-0

$$f(x)=\log |\sin x|$$, where $$x \in(0, \pi)$$ is strictly increasing on

A
$$\left(\frac{\pi}{2}, \pi\right)$$ only
B
$$(0, \pi)$$ only
C
$$\left(0, \frac{\pi}{2}\right)$$ only
D
$$\left(\frac{\pi}{4}, \frac{3 \pi}{4}\right)$$ only
2
MHT CET 2021 24th September Morning Shift
+2
-0

The velocity of a particle at time $$t$$ is given by the relation $$v=6 t-\frac{t^2}{6}$$. Its displacement S is zero at $$\mathrm{t}=0$$, then the distance travelled in $$3 \mathrm{~sec}$$ is

A
$$\frac{51}{2}$$ units
B
$$\frac{39}{2}$$ units
C
$$\frac{57}{2}$$ units
D
$$\frac{33}{2}$$ units
3
MHT CET 2021 23rd September Evening Shift
+2
-0

The radius of a circular plate is increasing at the rate of $$0.01 \mathrm{~cm} / \mathrm{sec}$$, when the radius is $$12 \mathrm{~cm}$$. Then the rate at which the area increases is

A
$$60 ~\pi \mathrm{~sq} . \mathrm{cm} / \mathrm{sec}$$
B
$$0.24 ~\pi \mathrm{~sq} . \mathrm{cm} / \mathrm{sec}$$
C
$$1.2 ~\pi \mathrm{~sq} . \mathrm{cm} / \mathrm{sec}$$
D
$$24 ~\pi \mathrm{~sq} . \mathrm{cm} / \mathrm{sec}$$
4
MHT CET 2021 23rd September Evening Shift
+2
-0

If $$x=a(\theta+\sin \theta)$$ and $$y=a(1-\cos \theta)$$ then $$\left(\frac{d^2 y}{d x^2}\right)_{at~ \theta=\pi / 2}=$$

A
$$\frac{a}{2}$$
B
$$\frac{1}{\mathrm{a}}$$
C
$$\mathrm{a}$$
D
$$2 \mathrm{a}$$
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