If $\mu_0$ and $\varepsilon_0$ are the permeability and permittivity of free space,respectively,then the dimension of $\left(\frac{1}{\mu_0 \varepsilon_0}\right)$ is

$A$ 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 $\%$)

Force $F$ is given by the equation $F = \frac{X}{\text{Linear density}}$. Then the dimensions of $X$ are:

The equation for a real gas is given by $(P + \frac{a}{V^2})(V - b) = RT$,where $P, V, T$ and $R$ are the pressure,volume,temperature,and gas constant,respectively. The dimension of $ab^{-2}$ is equivalent to that of

If the orbital velocity of a planet is given by $v = G^a M^b R^c$,then:

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