If ${\mu _0}$ and ${\varepsilon _0}$ denote the permeability and permittivity of free space,the dimensions of ${\mu _0}{\varepsilon _0}$ are:

$A$ quantity $z$, to be estimated, has a dependency on the variables $a, b$ and $c$ as $z = a b^2 c^{-2}$. The percentage errors in the measurement of $a, b$ and $c$ are $2.1 \%$, $1.3 \%$ and $2.2 \%$, respectively. The percentage error in the measurement of $z$ would then be: (in $\%$)

An expression for a dimensionless quantity $P$ is given by $P = \frac{\alpha}{\beta} \log_{e} \left( \frac{kt}{\beta x} \right)$,where $\alpha$ and $\beta$ are constants,$x$ is distance,$k$ is the Boltzmann constant,and $t$ is the temperature. Then the dimensions of $\alpha$ will be:

Assertion $(A) :$ Physical relations involving addition and subtraction cannot be derived by dimensional analysis.
Reason $(R) :$ Numerical constants cannot be deduced by the method of dimensions.

If $C$ (the velocity of light), $h$ (Planck's constant), and $G$ (gravitational constant) are taken as fundamental quantities, then the dimensional formula of mass is

If velocity $v$,acceleration $A$,and force $F$ are chosen as fundamental quantities,then the dimensional formula of angular momentum in terms of $v, A$,and $F$ would be