$(A)$: Using $\quad L = mvr =\frac{ nh }{2 \pi}$

Thus the angular momentum (L) has the same dimensions as that of Planck's constant (h)

$(B)$: Impulse $I =\Delta P$

Thus impulse $(I)$ has the same dimensions as that of linear momentum $(P)$

$(C)$: Using $\tau=I \alpha \quad \Rightarrow I=\frac{\tau}{\alpha}$

where angular acceleration is not dimensionless.

Thus the dimensions of moment of inertia are different from those of

moment of force

(OR torque)

$(D):$ Dimension of energy $E =\left[ ML ^2 T ^{-2}\right]$

Dimension of torque $\tau= Fr =\left[ ML ^2 T ^{-2}\right]$

Hence, torqua and energy have same dimensions.