If 2 moles of diatomic gas and 1 mole of monatomic gas are mixed, then the ratio of specific heats for the mixture is

${\mathrm{\mu }}_1=1,{\mathrm{\gamma }}_1=5/3$ (for monatomic gas) and ${\mathrm{\mu }}_2=2,{\mathrm{\gamma }}_2=7/5$ (for diatomic gas).

From formula

${\mathrm{\gamma }}_{\text{mixture }}=\frac{\frac{{\mathrm{\mu }}_1{\mathrm{\gamma }}_1}{{\mathrm{\gamma }}_1-1}+\frac{{\mathrm{\mu }}_2{\mathrm{\gamma }}_2}{{\mathrm{\gamma }}_2-1}}{\frac{{\mathrm{\mu }}_1}{{\mathrm{\gamma }}_1-1}+\frac{{\mathrm{\mu }}_2}{{\mathrm{\gamma }}_2-1}}=\frac{\frac{1\times \frac{5}{3}}{\frac{5}{3}-1}+\frac{2\times \frac{7}{5}}{\frac{7}{5}-1}}{\frac{1}{\frac{5}{3}-1}+\frac{2}{\frac{7}{5}-1}}=\frac{\frac{5}{2}+7}{\frac{3}{2}+5}=\frac{19}{13}$