To find the dimensions of Planck's constant and angular momentum, we examine their defining equations:

1. Planck's Constant ($h$): According to Planck's quantum theory, the energy ($E$) of a quantum of radiation is given by $E = h\nu$, where $\nu$ is the frequency . From the sources, energy has the dimensions $[ML^2T^{-2}]$ and frequency has the dimension $[T^{-1}]$ . Therefore, the dimensions of $h$ are $[ML^2T^{-2}] / [T^{-1}] = [ML^2T^{-1}]$ .

2. Angular Momentum ($L$): Angular momentum is defined as the product of mass ($m$), velocity ($v$), and radius ($r$), expressed as $L = mvr$ . Mass has the dimension $[M]$, velocity has dimensions $[LT^{-1}]$, and radius has the dimension $[L]$. Thus, the dimensions of angular momentum are $[M] \times [LT^{-1}] \times [L] = [ML^2T^{-1}]$ .

Since both physical quantities share the same dimensional formula, the correct pair is $[ML^2 T^{-1}]$ and $[ML^2 T^{-1}]$, which corresponds to Option B.