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:

A massive black hole of mass $m$ and radius $R$ is spinning with angular velocity $\omega$. The power $P$ radiated by it as gravitational waves is given by $P=G c^{-5} m^{x} R^{y} \omega^{z}$, where $c$ and $G$ are speed of light in free space and the universal gravitational constant, respectively. Then,

If force $(F),$ velocity $(V)$ and time $(T)$ are taken as fundamental units, then the dimensions of mass are 

The speed of light $(c)$, gravitational constant $(G)$ and planck's constant $(h)$ are taken as fundamental units in a system. The dimensions of time in this new system should be

Consider following statements

$(A)$ Any physical quantity have more than one unit

$(B)$ Any physical quantity have only one dimensional formula

$(C)$ More than one physical quantities may have same dimension

$(D)$ We can add and subtract only those expression having same dimension

Number of correct statement is

Which of the following is not a dimensionless quantity?