$A$ man of height $2 \ m$ walks at a uniform speed of $7 \ m/min$ away from a lamp post of height $9 \ m$. The rate (in $m/min$) at which the length of his shadow increases is

$A$ balloon,which always remains spherical on inflation,is being inflated by pumping in $900 \, cm^3$ of gas per second. Find the rate at which the radius of the balloon increases when the radius is $15 \, cm$.

$A$ particle covers a distance $x$ in time $t$ given by $x = t^3 - 9t^2 + 24t + 6$. When the acceleration of the particle is $6$,its velocity is .... units.

The height of a right circular cylinder is decreasing while its diameter is increasing at a rate of $4 \text{ cm/s}$ so as to keep its volume unchanged. The rate of change in its lateral surface area (in $\text{cm}^2/\text{s}$) at the instant when its diameter is $8 \text{ cm}$ and height is $12 \text{ cm}$,is (in $\pi$)

The surface area of a spherical balloon is increasing at the rate of $2 \text{ cm}^2/\text{sec}$. Find the rate of increase in the volume of the balloon when the radius of the balloon is $6 \text{ cm}$.

The motion of a stone thrown vertically upward is given by $s = 13.8t - 4.9t^2$,where $s$ is in meters and $t$ is in seconds. Then its velocity at $t = 1$ second is ........ $m/s$.