Dimensions of the quantity $\frac{p}{\varepsilon_0 \mu_0}$, where $p$ is the pressure, $\varepsilon_0$ is the electric permittivity of free space, and $\mu_0$ is the permeability of free space, will be:

Identify the incorrect statement.

The diameter of a wire measured by a screw gauge of least count $0.001 \text{ cm}$ is $0.08 \text{ cm}$. The length measured by a scale of least count $0.1 \text{ cm}$ is $150 \text{ cm}$. When a weight of $100 \text{ N}$ is applied to the wire, the extension in length is $0.5 \text{ cm}$, measured by a micrometer of least count $0.001 \text{ cm}$. The error in the measured Young's modulus is $\alpha \times 10^9 \text{ N/m}^2$. The value of $\alpha$ is . . . . . . . (Ignore the contribution of the load to Young's modulus error calculation)

In an experiment of measuring the refractive index of a glass slab using a travelling microscope in a physics lab,a student measures the real thickness of the glass slab as $5.25\,mm$ and the apparent thickness of the glass slab as $5.00\,mm$. The travelling microscope has $20$ divisions in $1\,cm$ on the main scale,and $50$ divisions on the Vernier scale are equal to $49$ divisions on the main scale. The estimated uncertainty in the measurement of the refractive index of the slab is $\frac{x}{10} \times 10^{-3}$,where $x$ is $..............$

In the following list,the only pair which has different dimensions is

The equation of state of a gas is given by $\left( P + \frac{aT^2}{V} \right) V^c = (RT + b)$,where $a, b, c$ and $R$ are constants. The isotherms can be represented by $P = AV^m - BV^n$,where $A$ and $B$ depend only on temperature. Then: