$A$ 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 .......... $m/s$.

$A$ point $P$ is moving on the curve $x^3 y^4 = 2^7$. The $x$-coordinate of $P$ is decreasing at the rate of $8 \text{ units per second}$. When the point $P$ is at $(2, 2)$, the $y$-coordinate of $P$:

The volume of a sphere is increasing at the rate of $1200 \text{ cm}^3/\text{s}$. The rate of increase in its surface area when the radius is $10 \text{ cm}$ is: (in $\text{ cm}^2/\text{s}$)

The two equal sides of an isosceles triangle with a fixed base $b$ are decreasing at the rate of $3 \ cm/s$. How fast is the area decreasing when the two equal sides are equal to the base?

$A$ stone is dropped in a quiet lake and it is observed that waves move in circles. If the radius of a circular wave increases at the rate of $2 \text{ cm/sec}$, then the rate of increase in its area at the instant when its radius is $10 \text{ cm}$, is in $\text{cm}^2\text{/sec}$: (in $\pi$)

The volume of a spherical ball is increasing at a rate of $4 \pi \text{ cm}^3 \text{ s}^{-1}$. The rate at which its radius increases,when its volume is $288 \pi \text{ cm}^3$,is ....... $\text{cm s}^{-1}$.