The pair of electrolytes that posses same value for the constant \((A)\) in the Debye-Huckel-Onsager equation, \(\Lambda_{m}=\Lambda_{m}^{\circ}-A \sqrt{C}\) is

\(\Lambda_{m}=\Lambda_{m}^{\circ}-A \sqrt{C}\)
Out of all the given pairs, the pair having same (similar) charges will possess the same value of \(A\). Here, \(\mathrm{MgSO}_{4}\) and \(\mathrm{Na}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{Mg}^{2+}\) and \(\mathrm{Na}^{+}\)
\(\mathrm{NH}_{4} \mathrm{Cl}\) and \(\mathrm{NaBr} \rightarrow \mathrm{NH}_{4}^{+}\)and \(\mathrm{Na}^{+}\)
\(\mathrm{NaBr}\) and \(\mathrm{MgSO}_{4} \rightarrow \mathrm{Na}^{+}\)and \(\mathrm{Mg}^{2+}\)
\(\mathrm{NaCl}\) and \(\mathrm{CaCl}_{2} \rightarrow \mathrm{Na}^{+}\)and \(\mathrm{Ca}^{2+}\)
So, only in \(\mathrm{NH}_{4} \mathrm{Cl}\) and \(\mathrm{NaBr}\), the charge is same on both the cations and hence, there will have same value of \(A\).