c
(c)
$Y$ for monatomic gas $=1+\frac{2}{3}=\frac{5}{3}=\gamma_1$
$\frac{n}{\gamma-1}=\frac{n_1}{\gamma_1-1}+\frac{n_2}{\gamma_2-1}$
$Y$ for diatomic gas $=1+\frac{2}{5}=\frac{7}{5}=\gamma_2$
$\frac{2}{\gamma-1}=\frac{1}{\frac{5}{3}-1}+\frac{1}{\frac{7}{5}-1}$
Solving, we get $\gamma=3 / 2$