1
MHT CET 2021 22th September Morning Shift
+2
-0

The point on the curve $$y^2=2(x-3)$$ at which the normal is parallel to the line $$y-2 x+1=0$$ is

A
$$\left(\frac{-1}{2},-2\right)$$
B
$$\left(\frac{3}{2}, 2\right)$$
C
$$(5,2)$$
D
$$(5,-2)$$
2
MHT CET 2021 22th September Morning Shift
+2
-0

A sperical snow ball is forming so that its volume is increasing at the rate of $$8 \mathrm{~cm}^3 / \mathrm{sec}$$. Find the rate of increase of radius when radius is $$2 \mathrm{~cm}$$.

A
$$\pi ~\mathrm{cm} / \mathrm{sec}$$.
B
$$\frac{1}{8 \pi} ~\mathrm{cm} / \mathrm{sec}$$.
C
$$2 \pi ~\mathrm{cm} / \mathrm{sec}$$.
D
$$\frac{1}{2 \pi} ~\mathrm{cm} / \mathrm{sec}$$.
3
MHT CET 2021 21th September Evening Shift
+2
-0

The abscissa of the points, where the tangent to the curve $$y=x^3-3 x^2-9 x+5$$ is parallel to $$X$$ axis are

A
$$x=1$$ and $$-1$$
B
$$x=1$$ and $$-3$$
C
$$x=-1$$ and 3
D
$$\mathrm{x}=0$$ and 1
4
MHT CET 2021 21th September Evening Shift
+2
-0

For all real $$x$$, the minimum value of the function $$f(x)=\frac{1-x+x^2}{1+x+x^2}$$ is

A
$$\frac{1}{3}$$
B
0
C
3
D
1
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