Match List-I with List-II. List-I List-II (A) Planck's constant /...

Let us find the dimensional formula for each ratio in List-I:

(A) Planck's constant ($h$) / Moment of inertia ($I$):
$[h] = [M L^2 T^{-1}]$ and $[I] = [M L^2]$
Ratio $= \dfrac{[M L^2 T^{-1}]}{[M L^2]} = [M^0 L^0 T^{-1}]$ (Matches with II)

(B) Pressure ($P$) / Density ($\rho$):
$[P] = [M L^{-1} T^{-2}]$ and $[\rho] = [M L^{-3}]$
Ratio $= \dfrac{[M L^{-1} T^{-2}]}{[M L^{-3}]} = [M^0 L^2 T^{-2}]$ (Matches with III)

(C) Energy ($E$) / Gravitational constant ($G$):
$[E] = [M L^2 T^{-2}]$ and $[G] = [M^{-1} L^3 T^{-2}]$
Ratio $= \dfrac{[M L^2 T^{-2}]}{[M^{-1} L^3 T^{-2}]} = [M^2 L^{-1} T^0]$ (Matches with I)

(D) Coefficient of viscosity ($\eta$) / Density ($\rho$):
$[\eta] = [M L^{-1} T^{-1}]$ and $[\rho] = [M L^{-3}]$
Ratio $= \dfrac{[M L^{-1} T^{-1}]}{[M L^{-3}]} = [M^0 L^2 T^{-1}]$ (Matches with IV)

Therefore, the correct matching is (A)-(II), (B)-(III), (C)-(I), (D)-(IV).

Answer: (A)-(II), (B)-(III), (C)-(I), (D)-(IV)