$A$ bullet is shot horizontally and its distance $S$ cm at time $t$ second is given by $S=1200t-15t^2$. Then, the distance covered by the bullet when it comes to rest is: (in $\text{ cm}$)

Each edge of a cube is expanding at the rate of $1 \text{ cm/sec}$. Then the rate (in $\text{cc/sec}$) of change in its volume,when each of its edge is of length $5 \text{ cm}$,is

The total cost $C(x)$ in Rupees,associated with the production of $x$ units of an item is given by $C(x) = 0.005x^{3} - 0.02x^{2} + 30x + 5000$. Find the marginal cost when $3$ units are produced,where marginal cost is defined as the instantaneous rate of change of total cost with respect to the number of units produced.

If $y = x - x^2$,then the rate of change of $y^2$ with respect to $x^2$ at $x = 2$ is

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

$A$ balloon,which always remains spherical,has a variable diameter of $ \frac{3}{2}(2x + 3) $. Find the rate of change of its volume with respect to $ x $.