Gas is being pumped into a spherical balloon at the rate of $30 \, ft^3/min$. The rate at which the radius increases when it reaches the value $15 \, ft$ is:

$A$ particle moves in a straight line such that $s = \sqrt{t}$,then its acceleration is proportional to

The speed $v$ of a particle moving along a straight line is given by $a + b{v^2} = {x^2}$ (where $x$ is its distance from the origin). The acceleration of the particle is

In a $\triangle ABC$, the sides $b$ and $c$ are fixed. If there is an error of $\delta A$ in measuring angle $A$, then the percentage error in measuring the length of the side $a$ is:

$A$ street light is at the top of a $12 \ m$ pole. $A$ man $2 \ m$ tall walks away from the pole towards a wall $12 \ m$ away from the pole at a speed of $1/2 \ m/s$. The rate at which his shadow on the wall is decreasing when he is $8 \ m$ from the wall is:

The vertical angle of a right circular cone is $60^{\circ}$. If water is being poured into the cone at the rate of $\frac{1}{\sqrt{3}} \text{ m}^3/\text{min}$, then the rate $(\text{m/min})$ at which the radius of the water level is increasing when the height of the water level is $3 \text{ m}$ is