1
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

An object is moving in the clockwise direction around the unit circle $$x^2+y^2=1$$. As it passes through the point $$\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$$, its $$y$$-co-ordinate is decreasing at the rate of 3 units per sec. The rate at which the $$x$$-co-ordinate changes at this point is

A
2 units/sec
B
$$3 \sqrt{3}$$ units/sec
C
$$\sqrt{3}$$ units /sec
D
$$2 \sqrt{3}$$ units /sec
2
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A spherical raindrop evaporates at a rate proportional to its surface area. If originally its radius is $$3 \mathrm{~mm}$$ and 1 hour later it reduces to $$2 \mathrm{~mm}$$, then the expression for the radius $$R$$ of the raindrop at any time $$t$$ is

A
$$6 \mathrm{R}=\mathrm{t}+2$$
B
$$\mathrm{R}(\mathrm{t}+2)=6$$
C
$$\mathrm{R}=6(\mathrm{t}+2)$$
D
$$6 \mathrm{R}=\mathrm{t}$$
3
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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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