Two cylinders $A$ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at $300\mathrm{K}$. The piston of $A$ is free to move while that of $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $30\mathrm{K}$, then the rise in temperature of the gas in $B$ is

For cylinder $A$, the piston is free, so heating is at constant pressure. For cylinder $B$, the piston is fixed, so heating is at constant volume. Since the same heat is supplied to equal moles of the same gas, $$Q_A = nC_P\Delta T_A$$ $$Q_B = nC_V\Delta T_B$$ and given $Q_A = Q_B$, $$nC_P\Delta T_A = nC_V\Delta T_B$$ $$\Delta T_B = \frac{C_P}{C_V}\Delta T_A$$ For an ideal diatomic gas at this temperature, $$C_V = \frac{5R}{2}$$ $$C_P = \frac{7R}{2}$$ So, $$\Delta T_B = \frac{7/2}{5/2} \times 30$$ $$\Delta T_B = \frac{7}{5} \times 30 = 42\mathrm{K}$$ This matches option $D$.