Two solutions of electrolytes $X$ and $Y$ are taken in two beakers and diluted by adding $500 \ mL$ of water. The molar conductivity $(\Lambda_m)$ of $X$ increases by $1.5$ times,while that of $Y$ increases by $20$ times. What could be the electrolytes $X$ and $Y$?

Resistance of $0.05 \ M$ electrolytic solution at $298 \ K$ temperature is $30.0 \ \Omega$. The cross-sectional area of the conductivity cell having $Pt$ electrodes is $3.8 \ cm^{2}$ and the distance between the two electrodes is $1.5 \ cm$. What is the molar conductivity of the electrolytic solution?

Molar conductivity of $0.01 \ M$ $HCl$ solution is $400.0 \ \Omega^{-1} \ cm^{2} \ mol^{-1}$. Calculate the conductivity of $HCl$ solution.

When a certain conductivity cell was filled with $0.1 \ M \ KCl$,it had a resistance of $85 \ \Omega$ at $25 \ ^oC$. When the same cell was filled with an aqueous solution of $0.052 \ M$ unknown electrolyte,the resistance was $96 \ \Omega$. Calculate the molar conductivity of the unknown electrolyte at this concentration ............. $\Omega^{-1} \ cm^2 \ mol^{-1}$ (Given: Specific conductance of $0.1 \ M \ KCl = 1.29 \times 10^{-2} \ \Omega^{-1} \ cm^{-1}$)

Specific conductance of $0.2 \ M$ electrolyte solution at $20 \ ^oC$ temperature is $2.48 \times 10^{-4} \ ohm^{-1} \ cm^{-1}$. The molar conductance of the solution will be ............ $ohm^{-1} \ cm^2 \ mol^{-1}$.

The values of $\lambda^{\infty}_m$ for $NH_4Cl$,$NaOH$,and $NaCl$ are $129.8$,$248.1$,and $126.4 \ \Omega^{-1} \ cm^2 \ mol^{-1}$ respectively. Calculate $\lambda^{\infty}_m$ for $NH_4OH$ solution (in $\Omega^{-1} \ cm^2 \ mol^{-1}$).