The surface of water in a water tank of cross section area $750 \mathrm{~cm}^2$ on the top of a house is ' $h$ ' $m$ above the tap level. The speed of water coming out through the tap of cross section area $500 \mathrm{~mm}^2$ is $30 \mathrm{~cm} / \mathrm{s}$. At that instant $\frac{\mathrm{dh}}{\mathrm{dt}}$ is $x=10^{-3} \mathrm{~m} / \mathrm{s}$. The value of ' $x$ ' will be

A string A has twice the length, twice the diameter, twice the tension and twice the density of another string B. The overtone of A which will have the same fundamental frequency as that of $B$ is

An inductor of inductance $2 \mu \mathrm{H}$ is connected in series with a resistance, a variable capacitor and an a.c. source of frequency 5 kHz . The value of capacitance for which maximum current is drawn into the circuit is $\frac{1}{\mathrm{x}} \mathrm{F}$, where the value of ' $x$ ' is (Take $\pi^2=10$)

Three identical polaroids $P_1, P_2$ and $P_3$ are placed one after another. The pass axis of $P_2$ and $P_3$ are inclined at an angle $60^{\circ}$ and $90^{\circ}$ with respect to axis of $P_1$. The source has an intensity $I_0$. The intensity of transmitted light through $P_3$ is $\left(\cos 60^{\circ}=0.5, \cos 30^{\circ}=\frac{\sqrt{3}}{2}\right)$