JEE Advanced 2025 · Paper 1, Chemistry question 10

Molar volume ($V_m$) of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with $V_m$ as the variable. The ratio (in $\mathrm{mol\,dm^{-3}}$) of the coefficient of $V_m^2$ to the coefficient of $V_m$ for a gas having van der Waals constants $a = 6.0\ \mathrm{dm^6\,atm\,mol^{-2}}$ and $b = 0.060\ \mathrm{dm^3\,mol^{-1}}$ at 300 K and 300 atm is _____.

Use: Universal gas constant (R) $= 0.082\ \mathrm{dm^3\,atm\,mol^{-1}\,K^{-1}}$