Identify the pair of physical quantities that have same dimensions:

We need to identify which pair of physical quantities have the same dimensions.

For option A, velocity gradient and decay constant are considered. Velocity gradient is defined as the rate of change of velocity with respect to distance: $$\text{Velocity gradient} = \frac{dv}{dx}$$ Its dimensions are: $$\frac{[LT^{-1}]}{[L]} = [T^{-1}]$$ Decay constant $$\lambda$$ appears in the radioactive decay law $$N = N_0 e^{-\lambda t}$$ and since $$\lambda t$$ must be dimensionless, $$[\lambda] = [T^{-1}]$$ Both have dimensions $$[T^{-1}]$$ and therefore match.

For option B, angular frequency $$\omega$$ has dimensions $$[T^{-1}]$$, while angular momentum $$L = I\omega$$ has dimensions $$[ML^2T^{-1}]$$. These are different.

For option C, wave number $$k = 1/\lambda$$ has dimensions $$[L^{-1}]$$, while Avogadro number $$N_A$$ has dimensions $$[\text{mol}^{-1}]$$. These are different.

For option D, Wien's displacement constant $$b$$ has dimensions $$[LK]$$ (from $$\lambda_{max} T = b$$), while Stefan's constant $$\sigma$$ has dimensions $$[MT^{-3}K^{-4}]$$ (from $$P = \sigma A T^4$$). These are different.

Therefore, the correct answer is Option A: Velocity gradient and decay constant both have dimensions $$[T^{-1}]$$.