JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Equilibrium

Take the statements one at a time. For the strong-acid strong-base mixture the diprotic $\mathrm{H}{}_2\mathrm{SO}{}_4$ supplies $80$ mmol of $\mathrm{H}{}^{+}$ and the $\mathrm{NaOH}$ neutralises $40$ mmol, leaving $40$ mmol of $\mathrm{H}{}^{+}$ in $800$ mL, so $[\mathrm{H}{}^{+}]=\frac{40}{800}=0.05$ M and $\mathrm{pH}=-\log (0.05)\approx 1.3$, so statement (a) holds. That $K_w$ changes with temperature is also correct, since the self-ionisation of water is temperature dependent. For the weak acid with $K_a=10^{-5}$ at $\mathrm{pH}=5$, $[\mathrm{H}{}^{+}]=10^{-5}=c\alpha$, and combining this with $K_a=\frac{c{\alpha }^2}{1-\alpha }$ gives $\alpha =0.5$, a $50\%$ dissociation, which holds too. The remaining statement, denying that Le Chatelier's principle governs the common-ion effect, is the false one, so three of the four statements stand.