b
${({C_P})_{mix}} = \frac{{{\mu _1}{C_{{P_1}}} + {\mu _2}{C_{{P_2}}}}}{{{\mu _1} + {\mu _2}}}$(${C_{{P_1}}}(He) = \frac{5}{2}R$ and ${C_{{P_2}}}({H_2}) = \frac{7}{2}R$)
$ = \frac{{1 \times \frac{5}{2}R + 1 \times \frac{7}{2}R}}{{1 + 1}}$= 3R$ = 3 \times 2 = 6\,cal/mol.^\circ C$
Heat required to raise the temperature from $0^{o}C$ to $100^{o}C$
${(\Delta Q)_P} = \mu {C_P}\Delta T = 2 \times 6 \times 100 = 1200\,cal$