Which among the following salts forms basic solution in water?

The acidity or basicity of a salt solution depends on the hydrolysis behavior of its constituent ions, governed by the relative strengths of the parent acid and base.

Classification of salt types:

Salts of strong acid–strong base pairs produce neutral solutions, weak acid–strong base pairs yield basic solutions, strong acid–weak base pairs yield acidic solutions, and weak acid–weak base pairs exhibit pH dependent on the relative magnitudes of $K_a$ and $K_b$.

Case analysis:

For $\mathrm{NH}_4\mathrm{NO}_3$: derived from weak base $\mathrm{NH}_3$ and strong acid $\mathrm{HNO}_3$, $\mathrm{NH}_4^+$ hydrolyzes via $\mathrm{NH}_4^+ (aq) + \mathrm{H}_2\mathrm{O} (l) \rightleftharpoons \mathrm{NH}_3 (aq) + \mathrm{H}_3\mathrm{O}^+ (aq)$, yielding an acidic solution.

For $\mathrm{Na}_2\mathrm{CO}_3$: derived from strong base $\mathrm{NaOH}$ and weak acid $\mathrm{H}_2\mathrm{CO}_3$, $\mathrm{CO}_3^{2-}$ hydrolyzes via $\mathrm{CO}_3^{2-} (aq) + \mathrm{H}_2\mathrm{O} (l) \rightleftharpoons \mathrm{HCO}_3^- (aq) + \mathrm{OH}^- (aq)$, with potential further hydrolysis of $\mathrm{HCO}_3^-$, yielding a basic solution.

For $\mathrm{NH}_4\mathrm{Cl}$: derived similarly from weak base $\mathrm{NH}_3$ and strong acid $\mathrm{HCl}$, with $\mathrm{NH}_4^+$ hydrolysis yielding an acidic solution.

For $\mathrm{Na}_2\mathrm{SO}_4$: derived from strong base $\mathrm{NaOH}$ and strong acid $\mathrm{H}_2\mathrm{SO}_4$, with negligible hydrolysis, yielding a neutral solution.

Only $\mathrm{Na}_2\mathrm{CO}_3$ produces a basic solution.

$ \boxed{\text{B}} $