Which two of the following five physical parameters have the same dimensions?(a) energy density(b) refractive index(c) dielectric constant(d) Young's modulus(e) magnetic field

To find the physical parameters with the same dimensions, let's analyze each:Energy Density: It is defined as energy per unit volume.
$$[\text{Energy Density}]=\frac{[\text{Energy}]}{[\text{Volume}]}=\frac{[M{L}^2{T}^{-2}]}{[L^3]}=[M{L}^{-1}{T}^{-2}]$$
Refractive Index ($n$): It is the ratio of the speed of light in a vacuum to the speed of light in a medium. It is a dimensionless quantity.
$$[n]=[M^0{L}^0{T}^0]$$
Dielectric Constant (${ϵ}_r$): It is the ratio of the permittivity of a substance to the permittivity of free space. It is also dimensionless.
$$[{ϵ}_r]=[M^0{L}^0{T}^0]$$
Young's Modulus ($Y$): It is the ratio of stress to strain. Since strain is dimensionless, the dimensions of $Y$ are the same as stress (force/area).
$$[Y]=\frac{[Force]}{[Area]}=\frac{[ML{T}^{-2}]}{[L^2]}=[M{L}^{-1}{T}^{-2}]$$
Magnetic Field ($B$): From the formula $F=qvB$, we have $B=\frac{F}{qv}$.
$$[B]=\frac{[ML{T}^{-2}]}{[IT\cdot L{T}^{-1}]}=[M{T}^{-2}{I}^{-1}]$$
Comparing these, Energy Density and Young's Modulus have the same dimensional formula: $[M{L}^{-1}{T}^{-2}]$.