The rate of change of the area of a circle with respect to its radius $r$ at $r = 2 \text{ cm}$ is:

If the rate of change of the area of a square $S$ is equal to its side length,and the rate of change of the side of $S$ is the same as that of a cube $C$,then the rate of change of the volume of $C$,at the time when its side length is $2$ units,will be ............ $units^3/sec$.

$A$ particle is moving in a straight line according to the equation $s = 45t + 11t^2 - t^3$. The time at which it will come to rest is ......... $sec$.

$A$ particle is moving in a straight line according to the formula $s = t^2 + 8t + 12$. If $s$ is measured in meters and $t$ is measured in seconds,then the average velocity of the particle in the third second is .......... $m/s$.

$A$ spherical balloon is filled with $4500\pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $72\pi$ cubic meters per minute,then the rate (in meters per minute) at which the radius of the balloon decreases $49$ minutes after the leakage began is:

The area of a square increases at the rate of $0.5 \text{ cm}^2/\text{sec}$. The rate at which its perimeter is increasing when the side of the square is $10 \text{ cm}$ long,is