Which two of the following five physical parameters have the same dimensions $?$
$(1)$ energy density
$(2)$ refractive index
$(3)$ dielectric constant
$(4)$ Young's modulus
$(5)$ magnetic field

The two principal thrusts in physics are

Units for constants in Column-$I$ and $SI$ unit is given in Column-$II$. Match the followings:

Column-$I$	Column-$II$
$(a)$ Wien's constant	$(i)$ $W m^{-2} K^{-4}$
$(b)$ Stefan-Boltzmann's constant	$(ii)$ $W m^{-1} K^{4}$
	$(iii)$ $m K$

Which of the following pairs of physical quantities does not have the same dimensional formula?

To determine the Young's modulus of a wire,the formula is $Y = \frac{FL}{A\Delta L}$,where $L$ is the length,$A$ is the area of cross-section of the wire,and $\Delta L$ is the change in length of the wire when stretched with a force $F$. The conversion factor to change the unit of Young's modulus from $CGS$ to $MKS$ system is $x \times 10^{-1} \ N/m^2$. Find the value of $x$.

Match List-$I$ with List-$II$.

List-$I$	List-$II$
$(a)$ Capacitance,$C$	$(i)$ $M^{1} L^{1} T^{-3} A^{-1}$
$(b)$ Permittivity of free space,$\varepsilon_{0}$	$(ii)$ $M^{-1} L^{-3} T^{4} A^{2}$
$(c)$ Permeability of free space,$\mu_{0}$	$(iii)$ $M^{-1} L^{-2} T^{4} A^{2}$
$(d)$ Electric field,$E$	$(iv)$ $M^{1} L^{1} T^{-2} A^{-2}$

Choose the correct answer from the options given below: