$A$ man $2 \, m$ high walks at a uniform speed of $5 \, m/h$ away from a lamp post $6 \, m$ high. The rate at which the length of his shadow increases is

$A$ spherical iron ball of radius $10 \, cm$ is coated with a layer of ice of uniform thickness that melts at a rate of $50 \, cm^3/min$. When the thickness of the ice is $5 \, cm$,then the rate at which the thickness (in $cm/min$) of ice decreases is

If the surface area of a spherical bubble is increasing at the rate of $4 \text{ cm}^2/\text{sec}$,then the rate of change in its volume (in $\text{cm}^3/\text{sec}$) when its radius is $8 \text{ cm}$ is:

The length and breadth of a rectangle are $x \text{ cm}$ and $y \text{ cm}$ respectively. If the length decreases at the rate of $5 \text{ cm/min}$ and the breadth increases at the rate of $3 \text{ cm/min}$,then the rates of change of the perimeter and area respectively when $x = 5 \text{ cm}$ and $y = 2 \text{ cm}$ are:

$A$ rod of length $41 \ ft$ with an end $A$ on the floor and another end $B$ on the wall perpendicular to the floor is sliding away horizontally from the wall at the rate of $3 \ ft/min$. When the end $B$ is at a height of $9 \ ft$ from the floor, the rate at which the area of the triangle formed by the rod with the wall and the floor changes at that instant is (in $ft^2/min$):

$A$ particle is moving on a straight line,where its position $s$ (in metre) is a function of time $t$ (in seconds) given by $s = at^2 + bt + 6, t \ge 0$. If it is known that the particle comes to rest after $4 \, s$ at a distance of $16 \, m$ from the starting position $(t = 0)$,then the retardation in its motion is