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:

Which of the following pairs is incorrectly matched?

Let $f(x)=15-|x-10| ; x \in R$. Then,the set of all values of $x$,at which the function $g(x)=f(f(x))$ is not differentiable,is

If $f(x) = \frac{1}{\sqrt{x + 2 \sqrt{2x - 4}}} + \frac{1}{\sqrt{x - 2 \sqrt{2x - 4}}}$ for $x > 2$,then $f(11)$ is equal to

$A$ series combination of $n_1$ capacitors,each of value $C_1$,is charged by a source of potential difference $4V$. When another parallel combination of $n_2$ capacitors,each of value $C_2$,is charged by a source of potential difference $V$,it has the same total energy stored in it as the first combination. The value of $C_2$,in terms of $C_1$,is:

If $\alpha, \beta, \gamma, \delta$ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity $k$,then the value of $4\sin \frac{\alpha}{2} + 3\sin \frac{\beta}{2} + 2\sin \frac{\gamma}{2} + \sin \frac{\delta}{2}$ is equal to