Two capillary tubes of same diameter are kept vertically in two liquids whose densities are in the ratio $4: 3$. If their surface tensions are in the ratio $6: 5$, the ratio of heights $\left(\frac{h_1}{h_2}\right)$ of liquids in the two capillary tubes is (Their angle of contacts are same)

An ideal inductor of $\left(\frac{1}{\pi}\right) \mathrm{H}$ is connected in series with a $300 \Omega$ resistor. If a $20 \mathrm{~V}, 200 \mathrm{~Hz}$ alternating source is connected across the combination, the phase difference between the voltage and current is

Hot water cools from $80^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ in 1 minutes. In cooling from $60^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$ it will take (room temperature $=30^{\circ} \mathrm{C}$ )

A Carnot engine has efficiency $\frac{1}{6}$. It becomes $\frac{1}{3}$, when the temperature of $\operatorname{sink}$ is lowered by

57 K . The temperature of the source is