Two ideal polyatomic gases at temperatures \(\boldsymbol{T}_{\mathbf{1}}\) and \(\boldsymbol{T}_{\mathbf{2}}\) are mixed…

Two ideal polyatomic gases at temperatures \(\boldsymbol{T}_{\mathbf{1}}\) and \(\boldsymbol{T}_{\mathbf{2}}\) are mixed so that there is no loss of energy. If \(\boldsymbol{F}_1\) and \(\boldsymbol{F}_2, \boldsymbol{m}_1\) and \(\boldsymbol{m}_2, \boldsymbol{n}_1\) and \(\boldsymbol{n}_2\) be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is:

[JEE Main 2021, 17 Mar (Shift 1)]