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
$\left[M^{-3} L^{-2} T^{4} Q^{4}\right]$
$\left[M L^{2} T^{8} Q^{4}\right]$
$\left[M^{-2} L^{-3} T^{2} Q^{4}\right]$
$\left[M^{-2} L^{-2} T Q^{2}\right]$
A physcial quantity $x$ depends on quantities $y$ and $z$ as follows: $x = Ay + B\tan Cz$, where $A,\,B$ and $C$ are constants. Which of the following do not have the same dimensions
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