$A$ gas mixture consists of $16 \ g$ of helium and $16 \ g$ of oxygen. For this mixture,the ratio $C_P/C_V$ is equal to:

$3$ moles of mono-atomic gas $(\gamma = 5/3)$ is mixed with $1$ mole of a diatomic gas $(\gamma = 7/5)$. The value of $\gamma$ for the mixture will be

$A$ mixture of ideal gas containing $5$ moles of monatomic gas and $1$ mole of rigid diatomic gas is initially at pressure $P_0$,volume $V_0$ and temperature $T_0$. If the gas mixture is adiabatically compressed to a volume $V_0 / 4$,then the correct statement$(s)$ is/are:
(Given $2^{1.2}=2.3$; $2^{3.2}=9.2$; $R$ is gas constant)
$(1)$ The final pressure of the gas mixture after compression is in between $9 P_0$ and $10 P_0$.
$(2)$ The average kinetic energy of the gas mixture after compression is in between $18 RT_0$ and $19 RT_0$.
$(3)$ The work $|W|$ done during the process is $13 RT_0$.
$(4)$ Adiabatic constant of the gas mixture is $1.6$.

$2 \text{ mole}$ of $N_2$ gas at $27 \, ^oC$ is mixed with $1 \text{ mole}$ of $He$ gas at $-73 \, ^oC$. Find the final temperature $T_{\text{mix}}$ of the mixture.

$A$ container has two chambers of volumes $V_1=2 \ L$ and $V_2=3 \ L$ separated by a partition made of a thermal insulator. The chambers contain $n_1=5$ and $n_2=4$ moles of an ideal gas at pressures $p_1=1 \ atm$ and $p_2=2 \ atm$,respectively. When the partition is removed,the mixture attains an equilibrium pressure of: (in $atm$)

$A$ gas mixture consists of molecules of $A, B$ and $C$ with masses $m_A > m_B > m_C$. Rank the three types of molecules in decreasing order of $(a)$ average $K.E.$,$(b)$ $rms$ speeds.