If velocity of light $c$, Planck’s constant $h$ and gravitational constant $G$ are taken as fundamental quantities, then express length in terms of dimensions of these quantities.

Time period $T\,\propto \,{P^a}\,{d^b}\,{E^c}$  then value of $c$ is  given $p$ is pressure, $d$ is density and $E$ is energy

The potential energy of a point particle is given by the expression $V(x)=-\alpha x+\beta \sin (x / \gamma)$. A dimensionless combination of the constants $\alpha, \beta$ and $\gamma$ is

The entropy of any system is given by

${S}=\alpha^{2} \beta \ln \left[\frac{\mu {kR}}{J \beta^{2}}+3\right]$

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 repectively. [Take ${S}=\frac{{dQ}}{{T}}$ ]

Choose the incorrect option from the following: