Chemistry Question from JEE Main 2023 · 25 January, Shift 1

A litre of buffer solution contains $0.1$ mole of each $\mathrm{NH_3}$ and $\mathrm{NH_4Cl}$. On addition of $0.02$ mole of $\mathrm{HCl}$, the pH of the solution is found to be _____ $\times 10^{-3}$ (Nearest integer).

Given: $\mathrm{p}K_b(\mathrm{NH_3}) = 4.745$; $\log 2 = 0.301$; $\log 3 = 0.477$; $T = 298 \, \text{K}$.