1
MHT CET 2023 9th May Morning Shift
+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
+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 2022 11th August Evening Shift
+2
-0

If the function $$f(x)=x^3-3(a-2) x^2+3 a x+7$$, for some $$a \in I R$$ is increasing in $$(0,1]$$ and decreasing in $$[1,5)$$, then a root of the equation $$\frac{f(x)-14}{(x-1)^2}=0(x \neq 1)$$ is

A
14
B
7
C
$$-$$14
D
$$-$$7
4
MHT CET 2022 11th August Evening Shift
+2
-0

A firm is manufacturing 2000 items. It is estimated that the rate of change of production $$P$$ with respect to additional number of workers $$x$$ is given by $$\frac{\mathrm{d} P}{\mathrm{~d} x}=100-12 \sqrt{x}$$. If the firm employs 25 more workers, then the new level of production of items is

A
4500
B
3000
C
2500
D
3500
EXAM MAP
Medical
NEET