Physics Question from JEE Main 2025 · 2 April, Shift 1

$\gamma_A$ is the specific heat ratio of monoatomic gas A having $3$ translational degrees of freedom. $\gamma_B$ is the specific heat ratio of polyatomic gas B having $3$ translational, $3$ rotational degrees of freedom and $1$ vibrational mode. If $\frac{\gamma_A}{\gamma_B} = \left( 1 + \frac{1}{n} \right)$ then the value of $n$ is _____.