In a particular system of units, a physical quantity can be expressed in terms of the electric charge $c$, electron mass $m_c$, Planck's constant $h$, and Coulomb's constant $k=\frac{1}{4 \pi \epsilon_0}$, where $\epsilon_0$ is the permittivity of vacuum. In terms of these physical constants, the dimension of the magnetic field is $[B]=[c]^\alpha\left[m_c\right]^\beta[h]^\gamma[k]^\delta$. The value of $\alpha+\beta+\gamma+\delta$ is. . . . .

If force $[F],$ acceleration $[A]$ and time $[T]$ are chosen as the fundamental physical quantities. Find the dimensions of energy.

If $x$  and $a$ stand for distance then for what value of $n$ is given equation dimensionally correct the eq. is  $\int {\frac{{dx}}{{\sqrt {{a^2}\, - \,{x^n}} \,}}\, = \,{{\sin }^{ - 1}}\,\frac{x}{a}} $

A quantity $f$ is given by $f=\sqrt{\frac{{hc}^{5}}{{G}}}$ where $c$ is speed of light, $G$ universal gravitational constant and $h$ is the Planck's constant. Dimension of $f$ is that of

In a new system of units energy $(E)$, density $(d)$ and power $(P)$ are taken as fundamental units, then the dimensional formula of universal gravitational constant $G$ will be .......

If $R , X _{ L }$. and $X _{ C }$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless: