$$\left(P + \frac{a}{V^2}\right)(V - b) = RT$$ represents the equation of state of some gases. Where $$P$$ is the pressure, $$V$$ is the volume, $$T$$ is the temperature and $$a, b, R$$ are the constants. The physical quantity, which has dimensional formula as that of $$\frac{b^2}{a}$$, will be :

Van der Waals equation: $$\left(P + \frac{a}{V^2}\right)(V - b) = RT$$.

Dimensions of $$a$$: $$[a] = [P][V^2] = [ML^{-1}T^{-2}][L^6] = [ML^5T^{-2}]$$.

Dimensions of $$b$$: $$[b] = [V] = [L^3]$$.

Dimensions of $$\frac{b^2}{a} = \frac{[L^6]}{[ML^5T^{-2}]} = [M^{-1}L^1T^2]$$.

Now check which physical quantity has dimensions $$[M^{-1}L^1T^2]$$:

Bulk modulus: $$[ML^{-1}T^{-2}]$$ - No.
Modulus of rigidity: $$[ML^{-1}T^{-2}]$$ - No.
Compressibility: $$\frac{1}{\text{Bulk modulus}} = [M^{-1}LT^2]$$ - Yes!
Energy density: $$[ML^{-1}T^{-2}]$$ - No.

The correct answer is Option C: Compressibility.