$A$ point moves in a straight line during the time $t = 0$ to $t = 3$ according to the law $s = 15t - 2t^2$. The average velocity is

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?

The point on the curve $6y = x^3 + 2$ at which the $y$-coordinate is changing $8$ times as fast as the $x$-coordinate 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:

The radius of a circular plate is increasing at the rate of $0.01 \text{ cm/sec}$. When the radius is $12 \text{ cm}$,the rate at which the area increases 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 $\frac{\pi}{6}$.