$A$ man of height $2 \text{ m}$ walks at a uniform speed of $5 \text{ km/h}$ away from a lamp post which is $6 \text{ m}$ high. Find the rate at which the length of his shadow increases. (in $\text{ km/h}$)

If the radius of a circle increases at the rate of $7 \text{ cm/sec}$,then the rate of increase of its area after $10 \text{ minutes}$ is:

Air is discharging from a large spherical balloon at the rate of $4 \,m^3 / min$. The rate at which the surface area is shrinking when the radius of the balloon is $8 \,m$, is

Water is dripping out at a steady rate of $1 \text{ cm}^3/\text{sec}$ through a tiny hole at the vertex of a conical vessel,whose axis is vertical. When the slant height of water in the vessel is $4 \text{ cm}$,find the rate of decrease of the slant height,where the semi-vertical angle of the conical vessel is $\frac{\pi}{6}$.

The volume of a spherical balloon is increasing at a rate of $40 \text{ cm}^3/\text{min}$. Find the rate of change of its surface area when its radius is $8 \text{ cm}$ (in $\text{cm}^2/\text{min}$).

The distance covered by a particle in $t$ seconds is given by $x = 3 + 8t - 4t^2$. After $1$ second,the velocity will be: