Consider the following physical quantities: Refractive index,...

Let us evaluate the dimensional formula for each given quantity:

1. Refractive index = $\dfrac{\text{Speed of light in vacuum}}{\text{Speed of light in medium}} \Rightarrow$ Dimensionless $[M^0 L^0 T^0]$
2. Relative density = $\dfrac{\text{Density of substance}}{\text{Density of water}} \Rightarrow$ Dimensionless $[M^0 L^0 T^0]$
3. Solid angle = $\dfrac{\text{Area}}{\text{Radius}^2} \Rightarrow$ Dimensionless $[M^0 L^0 T^0]$
4. Strain = $\dfrac{\text{Change in dimension}}{\text{Original dimension}} \Rightarrow$ Dimensionless $[M^0 L^0 T^0]$
5. Poisson's ratio = $\dfrac{\text{Lateral strain}}{\text{Longitudinal strain}} \Rightarrow$ Dimensionless $[M^0 L^0 T^0]$
6. Angular frequency = $\dfrac{\text{Angle}}{\text{Time}} \Rightarrow [M^0 L^0 T^{-1}]$
7. Pressure gradient = $\dfrac{\text{Pressure}}{\text{Distance}} \Rightarrow \dfrac{[M L^{-1} T^{-2}]}{[L]} = [M L^{-2} T^{-2}]$

There are exactly 5 dimensionless quantities in the given list.

Answer: 5