If $R$,$X_L$,and $X_C$ represent resistance,inductive reactance,and capacitive reactance respectively,then which of the following is dimensionless?

The ratio of the dimension of Planck's constant and that of moment of inertia is the dimension of

If $F_1, F_2$, and $F_3$ are the relative strengths of the gravitational, the weak nuclear, and the electromagnetic forces respectively, then

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:

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 $..............$

Some physical constants are given in List-$I$ and their dimensional formulae are given in List-$II$. Match the following:

List-$I$	List-$II$
$(1)$ Planck's constant	$(i)$ $[ML^{-1} T^{-2}]$
$(2)$ Gravitational constant	(ii) $[ML^{-1} T^{-1}]$
$(3)$ Bulk modulus	(iii) $[ML^2 T^{-1}]$
$(4)$ Coefficient of viscosity	(iv) $[M^{-1} L^3 T^{-2}]$

The correct answer is: