List of top Mathematics Questions on Rate of Change of Quantities asked in MHT CET

A spherical balloon is filled with (4500\pi) cubic meters of helium gas. If a leak causes gas to escape at (72\pi) m(^3)/min, then the rate at which the radius decreases 49 minutes after leakage began is

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

The rate of change of $\sqrt{x^{2}+16}$ with respect to $\frac{x}{x-1}$ at $x=5$ is

The diagonal of a square is changing at the rate of $0.5$ cm/sec. Then the rate of change of area when the area is $400$ cm$^{2}$ is equal to}

Let $B\equiv(0,3)$ and $C\equiv(4,0)$. The point A is moving on the line $y=2x$ at the rate of 2 units/second. The area of $\triangle ABC$ is increasing at the rate of