An aeroplane at an altitude of $1 \text{ km}$ is flying horizontally at $600 \text{ km/hr}$, passes directly over an observer. The rate at which it is approaching the observer when it is $1250 \text{ meters}$ away from him is........ (in $\text{ km/hr}$)

The total cost $C(x)$ in Rupees associated with the production of $x$ units of an item is given by $C(x) = 0.007x^{3} - 0.003x^{2} + 15x + 4000$. Find the marginal cost when $17$ units are produced.

Water is being filled at the rate of $1 \, cm^3/sec$ in a right circular conical vessel (vertex downwards) of height $35 \, cm$ and diameter $14 \, cm$. When the height of the water level is $10 \, cm$,the rate (in $cm^2/sec$) at which the wet conical surface area of the vessel increases is

$A$ horse runs along a circle with a speed of $20 \, km/hr$. $A$ lantern is at the centre of the circle. $A$ fence is along the tangent to the circle at the point at which the horse starts. The speed with which the shadow of the horse moves along the fence at the moment when it covers $1/8$ of the circle is (in $km/hr$):

$A$ ladder of length $10 \ m$ is resting against a vertical wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of $2 \ m/min$. How fast is its height on the wall decreasing when the foot of the ladder is $6 \ m$ away from the wall?

$A$ spherical iron ball of radius $10 \ cm$ is coated with a layer of ice of uniform thickness. The ice melts at a rate of $50 \ cm^3/min$. When the thickness of the ice is $5 \ cm$,the rate at which the thickness of the ice decreases is: