1
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
$$a=\frac{-1}{2}, b=\frac{-3}{4}, c=3$$
2
MHT CET 2021 24th September Evening Shift
+2
-0

The minimum value of the function f(x) = x log x is

A
$$-$$e
B
e
C
$$\frac{1}{e}$$
D
$$-\frac{1}{e}$$
3
MHT CET 2021 24th September Morning Shift
+2
-0

The maximum area of the rectangle that can be inscribed in a circle of radius $$r$$ is

A
$$2 r^2$$ sq. units
B
$$\frac{\pi \pi^2}{4}$$ sq. units
C
$$\pi r^2$$ units
D
$$r^3$$ sq units
4
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
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