The dimensions of $\frac{\alpha}{\beta}$ in the equation $F = \frac{\alpha - t^2}{\beta v^2}$,where $F$ is force,$v$ is velocity,and $t$ is time,are ..........

If the dimensional formula of $(\text{Energy} \times \text{speed})$ is $[M^{a} L^{b} T^{c}]$,then $a, b,$ and $c$ are:

Force $(F)$ and density $(d)$ are related as $F = \frac{\alpha}{\beta + \sqrt{d}}$. The dimensions of $\alpha$ are:

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.

$A$ neutron star with magnetic moment of magnitude $m$ is spinning with angular velocity $\omega$ about its magnetic axis. The electromagnetic power $P$ radiated by it is given by $\mu_{0}^{x} m^{y} \omega^{z} c^{u}$,where $\mu_{0}$ and $c$ are the permeability and speed of light in free space,respectively. Then,

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