Redox Reactions and Electrochemistry: JEE Main 2026 Chemistry question

The pH and conductance of a weak acid (HX) was found to be 5 and $4\times10^{-5}$ S, respectively. The conductance was measured under standard condition using a cell where the electrode plates having a surface area of 1 cm$^2$ were at a distance of 15 cm apart. The value of the limiting molar conductivity is ______ S m$^2$ mol$^{-1}$. (nearest integer) (Given : degree of dissociation of the weak acid ($\alpha$) << 1)