The Martians use force $(F)$, acceleration $(A)$ and time $(T)$ as their fundamental physical quantities. The dimensions of length on Martians system are

A gas bubble from an explosion under water oscillates with a period proportional of $P^a\,d^b\,E^c$ where $P$ is the static pressure, $d$ is the density of water and $E$ is the energy of explosion. Then $a,\,b$ and $c$ are

Applying the principle of homogeneity of dimensions, determine which one is correct. where $\mathrm{T}$ is time period, $\mathrm{G}$ is gravitational constant, $M$ is mass, $r$ is radius of orbit.

If the formula, $X=3 Y Z^{2}, X$ and $Z$ have dimensions of capacitance and magnetic induction. The dimensions of $Y$ in $M K S Q$ system are

The period of a body under SHM i.e. presented by $T = {P^a}{D^b}{S^c}$; where $P$ is pressure, $D$ is density and $S$ is surface tension. The value of $a,\,b$ and $c$ are

$A$ and $B$ possess unequal dimensional formula then following operation is not possible in any case:-