$A$ mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) is kept at room temperature $\left(27^{\circ} C\right)$. The ratio of the specific heat of these gases at constant volume is:

$Assertion :$ The ratio of $\frac{C_p}{C_v}$ for an ideal diatomic gas is less than that for an ideal monoatomic gas (where $C_p$ and $C_v$ have usual meaning).
$Reason :$ The atoms of a monoatomic gas have less degrees of freedom as compared to molecules of the diatomic gas.

Match the $\frac{C_{P}}{C_{v}}$ ratio for ideal gases with different types of molecules:

Molecule type	$\frac{C_{P}}{C_{v}}$
$A$. Monoatomic	$I$. $\frac{7}{5}$
$B$. Diatomic rigid molecules	$II$. $\frac{9}{7}$
$C$. Diatomic non-rigid molecules	$III$. $\frac{4}{3}$
$D$. Triatomic rigid molecules	$IV$. $\frac{5}{3}$

Which of the following statements is correct?

An ideal mono-atomic gas is taken through a process such that $dQ = 3dU$. The molar heat capacity for this process is: (in $R$)

The ratio of the adiabatic to isothermal elasticities of a triatomic gas is