The variation of molar conductivity with concentration of an electrolyte $X$ in aqueous solution is shown in the given figure.
The electrolyte $X$ is :

Resistance of a conductivity cell filled with $0.1 \, mol \, L^{-1}$ $KCl$ solution is $100 \, \Omega$. If the resistance of the same cell when filled with $0.02 \, mol \, L^{-1}$ $KCl$ solution is $520 \, \Omega$,calculate the conductivity and molar conductivity of $0.02 \, mol \, L^{-1} \, KCl$ solution. The conductivity of $0.1 \, mol \, L^{-1} \, KCl$ solution is $1.29 \, S / m$.

What is the cell constant of $\frac{N}{10}$ $KCl$ solution at $25^{\circ} C$,if conductivity and resistance of a solution is $0.0112 \ \Omega^{-1} cm^{-1}$ and $55.0 \ \Omega$ respectively (in $cm^{-1}$)?

The ionic conductivity of $Ba^{2+}$ and $Cl^{-}$ at infinite dilution are $127$ and $76 \ ohm^{-1} cm^2 eq^{-1}$ respectively. The equivalent conductivity of $BaCl_2$ at infinite dilution (in $ohm^{-1} cm^2 eq^{-1}$) would be $:-$

Ionic conductance of $Ga^{3+}$ ions and $NO_3^-$ ions at infinite dilution are $120 \, \Omega^{-1} \, cm^2 \, mol^{-1}$ and $50 \, \Omega^{-1} \, cm^2 \, mol^{-1}$ respectively. Equivalent conductance of $Ga(NO_3)_3$ at infinite dilution will be ........... $\Omega^{-1} \, cm^2 \, eq^{-1}$.

Conductivity of $0.001 \ M$ aqueous solution of $Na_2SO_4$ is found to be $2.6 \times 10^{-3} \ S \ cm^{-1}$ at $25 \ ^oC$. If limiting molar conductance of $Na^+$ is $50 \ S \ cm^2 \ mol^{-1}$,then limiting molar conductance of $SO_4^{2-}$ will be .............. $S \ cm^2 \ mol^{-1}$ (neglect conductivity of water).