$A$ man of height $2 \ m$ walks at a uniform speed of $5 \ km/hr$ away from a lamp post which is $6 \ m$ high. Find the rate at which the length of his shadow increases in $km/hr$.

The total cost $C(x)$ in Rupees, associated with the production of $x$ units of an item is given by $C(x) = 0.05x^3 - 0.2x^2 + 3x + 500$. The marginal cost, where $x = 3$ is $\rule{1cm}{0.15mm}$ (in Rupees).

$A$ man of height $1.8 \ m$ is moving away from a lamp post at the rate of $1.2 \ m/sec$. If the height of the lamp post is $4.5 \ m$,then the rate at which the shadow of the man is lengthening is .......... $m/sec$.

The rate of change of the volume of a sphere with respect to its surface area when the radius is $5 \ m$ 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:

The maximum height is reached in $5$ seconds by a stone thrown vertically upwards and moving under the equation $10s = 10ut - 49t^2$,where $s$ is in metres and $t$ is in seconds. The value of $u$ is ........ $m/sec$.