If $pv = 81$,then $\frac{dp}{dv}$ at $v = 9$ is equal to

If the displacement of a particle at a point is given by $s = 3t^{2} - 12t + 14$, then the displacement of the particle when its velocity becomes zero is (in $\text{ units}$)

$A$ balloon which always remains spherical is being inflated by pumping in $10 \text{ cm}^3$ of gas per second. Find the rate at which the radius of the balloon is increasing when the radius is $15 \text{ cm}$.

The equation of motion of a particle moving along a straight line is $s = 2t^{3} - 9t^{2} + 12t$,where the units of $s$ and $t$ are centimetre and second. The acceleration of the particle will be zero after: (in $s$)

$A$ water tank has the shape of an inverted right circular cone with its axis vertical and vertex lowermost. Its semi-vertical angle is $\tan ^{-1}(0.5)$. Water is poured into it at a constant rate of $5 \ m^3/h$. Find the rate at which the level of the water is rising at the instant when the depth of the water in the tank is $4 \ m$.

If the displacement,velocity,and acceleration of a particle at time $t$ are $x, v$,and $f$ respectively,then which of the following is true?