Thermodynamics: JEE Main 2021 Physics question

The entropy of any system is given by $S = {\alpha ^2}\beta \ln \left[ {{{\mu kR} \over {J{\beta ^2}}} + 3} \right]$ where $\alpha$ and $\beta$ are the constants. $\mu$, J, k and R are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant respectively. [Take $S = {{dQ} \over T}$] Choose the incorrect option from the following :