1
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
$$2 \mathrm{a}$$
2
MHT CET 2021 23rd September Evening Shift
+2
-0

The equation of tangent to the curve $$y=\sqrt{2} \sin \left(2 x+\frac{\pi}{4}\right)$$ at $$x=\frac{\pi}{4}$$, is

A
$$2 x+y-\frac{\pi}{2}-1=0$$
B
$$2 x-y-\frac{\pi}{2}+1=0$$
C
$$x+y-\frac{\pi}{2}-1=0$$
D
$$x-y-\frac{\pi}{2}+1=0$$
3
MHT CET 2021 23th September Morning Shift
+2
-0

Function $$f(x)=e^{-1 / x}$$ is strictly increasing for all $$x$$ where

A
$$x$$ is only positive real number
B
$$x$$ is only negative real number
C
$$x$$ is a real number
D
$$x$$ is a non-zero real number
4
MHT CET 2021 23th September Morning Shift
+2
-0

If $$x=-2$$ and $$x=4$$ are the extreme points of $$y=x^3-\alpha x^2-\beta x+5$$, then

A
$$\alpha=3, \beta=24$$
B
$$\alpha=-24, \beta=-3$$
C
$$\alpha=-3, \beta=-24$$
D
$$\alpha=24, \beta=3$$
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