Planck's constant $h$, speed of light $c$ and gravitational constant $G$ are used to form a unit of length $L$ and a unit of mass $M$. Then the correct option$(s)$ is(are)

$(A)$ $M \propto \sqrt{ c }$ $(B)$ $M \propto \sqrt{ G }$ $(C)$ $L \propto \sqrt{ h }$ $(D)$ $L \propto \sqrt{G}$

Time $(T)$, velocity $(C)$ and angular momentum $(h)$ are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be

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

If the speed of light $(c)$, acceleration due to gravity $(g)$ and pressure $(p)$ are taken as the fundamental quantities, then the dimension of gravitational constant is