Thank you for reporting, we will resolve it shortly
Q.
In an adiabatic process, the density of a diatomic gas becomes $32$ times its initial value. The final pressure of the gas is found to be $n$ times the initial pressure. The value of $n$ is:
In adiabatic proccss
$PV \gamma=$ constant
$P\left(\frac{m}{\rho}\right)^{\gamma}=$ constant
as mass is constant
$P \propto \rho^{\gamma}$
$\frac{P_{f}}{P_{i}}=\left(\frac{\rho_{f}}{\rho_{i}}\right)^{\gamma}$
$=(32)^{7 / 5}=2^{7}=128$