Column-$I$ represents the type of gas and Column-$II$ represents the ${C_P}$ value for that type of gas. Match them correctly:

Column-$I$	Column-$II$
$(a)$ Monoatomic gas	$(i)$ ${C_P} = \frac{3}{2}R$
$(b)$ Diatomic gas with vibration	$(ii)$ ${C_P} = \frac{5}{2}R$
	$(iii)$ ${C_P} = \frac{7}{2}R$
	$(iv)$ ${C_P} = \frac{9}{2}R$

(A) For a monoatomic gas, the degrees of freedom $f = 3$. The molar heat capacity at constant volume is ${C_V} = \frac{f}{2}R = \frac{3}{2}R$. Using Mayer's relation, ${C_P} = {C_V} + R = \frac{3}{2}R + R = \frac{5}{2}R$. Thus, $(a)$ matches with $(ii)$.
For a diatomic gas with vibration, the degrees of freedom $f = 7$ ($3$ translational + $2$ rotational + $2$ vibrational). The molar heat capacity at constant volume is ${C_V} = \frac{f}{2}R = \frac{7}{2}R$. Using Mayer's relation, ${C_P} = {C_V} + R = \frac{7}{2}R + R = \frac{9}{2}R$. Thus, $(b)$ matches with $(iv)$.
The correct matching is $(a-ii, b-iv)$.