$A$ 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

$A$ particle moves along the curve $6y = x^3 + 2$. Find the points on the curve at which the $y$-coordinate is changing $8$ times as fast as the $x$-coordinate.

If the radius $r$ of a sphere is increasing at a rate of $2 \text{ cm/s}$,then the rate of change of its surface area is proportional to which of the following?

$A$ ladder of $5 \ m$ long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of $3 \ m/sec$. The height of the upper end (in meters) while it is descending at the rate of $4 \ m/sec$,is

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

The volume of a ball is increasing at the rate of $4 \pi \text{ cc/sec}$. The rate of increase of the radius,when the volume is $288 \pi \text{ cc}$,is