$A$ man $2 \text{ m}$ tall walks at the rate of $1 \frac{2}{3} \text{ m/s}$ towards a street light which is $5 \frac{1}{3} \text{ m}$ above the ground. The rate at which the length of his shadow is changing when he is $3 \frac{1}{3} \text{ m}$ away from the base of the light is . . . . . . (in $\text{ m/s}$)

The displacement of a particle at the time $t$ is given by $s = \sqrt{1+t}$. Then its acceleration $a$ is proportional to:

$A$ right circular cone has height $9 \text{ cm}$ and radius of base $5 \text{ cm}$. It is inverted and water is poured into it. If at any instant, the water level rises at the rate $\frac{\pi}{A} \text{ cm/sec}$, where $A$ is the area of the water surface at that instant, then the cone is completely filled in: (in $\text{ sec}$)

The radius of a cylinder is increasing at the rate of $2 \text{ cm/sec}$ and its height is decreasing at the rate of $3 \text{ cm/sec}$. Find the rate of change of volume when the radius is $3 \text{ cm}$ and the height is $5 \text{ cm}$.

$A$ spherical balloon is expanding. If at any instant the rate of increase of its volume is $16$ times the rate of increase of its radius,then its radius at that instant is:

Water is being poured at the rate of $36 \ m^3/min$ into a cylindrical vessel,whose circular base has a radius of $3 \ m$. The rate at which the water level in the cylinder is rising is: