1
MHT CET 2023 11th May Evening Shift
+2
-0

$$A$$ rod $$A B, 13$$ feet long moves with its ends $$A$$ and $$B$$ on two perpendicular lines $$O X$$ and $$O Y$$ respectively. When $$A$$ is 5 feet from $$O$$, it is moving away at the rate of $$3 \mathrm{feet} / \mathrm{sec}$$. At this instant, $$\mathrm{B}$$ is moving at the rate

A
$$\frac{5}{4} \mathrm{ft} / \mathrm{sec}$$ upwards.
B
$$\frac{4}{5} \mathrm{ft} / \mathrm{sec}$$ upwards.
C
$$\frac{5}{4} \mathrm{ft} / \mathrm{sec}$$ downwards.
D
$$\frac{4}{5} \mathrm{ft} / \mathrm{sec}$$ downwards.
2
MHT CET 2023 11th May Evening Shift
+2
-0

The equation of the tangent to the curve $$y=\sqrt{9-2 x^2}$$, at the point where the ordinate and abscissa are equal, is

A
$$2 x+y+\sqrt{3}=0$$
B
$$2 x+y+3 \sqrt{3}=0$$
C
$$2 x-y-3 \sqrt{3}=0$$
D
$$2 x+y-3 \sqrt{3}=0$$
3
MHT CET 2023 11th May Evening Shift
+2
-0

At present a firm is manufacturing 1000 items. It is estimated that the rate of change of production $$\mathrm{P}$$ w.r.t. additional number of worker $$x$$ is given by $$\frac{\mathrm{dp}}{\mathrm{d} x}=100-12 \sqrt{x}$$. If the firm employees 9 more workers, then the new level of production of items is

A
1684
B
1648
C
2116
D
1116
4
MHT CET 2023 11th May Morning Shift
+2
-0

Value of $$c$$ satisfying the conditions and conclusions of Rolle's theorem for the function $$\mathrm{f}(x)=x \sqrt{x+6}, x \in[-6,0]$$ is

A
$$-4$$
B
4
C
3
D
$$-3$$
EXAM MAP
Medical
NEET