What is the conductivity of $0.05 \ M$ $KCl$ solution if cell constant is $1.32 \ cm^{-1}$ and resistance is $528 \ \Omega$?

The equivalent conductance of $1 \, M$ benzoic acid is $12.8 \, \text{mho} \, \text{cm}^2 \, \text{g-eq}^{-1}$. If the molar conductivities of benzoate ion and $H^+$ ion are $42$ and $288.42 \, \Omega^{-1} \, \text{cm}^2$ respectively,then the degree of dissociation is .......... $\%$.

Calculate the conductivity of $0.02 \ M$ electrolyte solution if its molar conductivity is $407.2 \ \Omega^{-1} \ cm^2 \ mol^{-1}$.

At $25\,^{\circ}C$,the molar conductivity at infinite dilution for electrolytes $KOH$,$KCl$ and $BaCl_2$ are $248 \times 10^{-4}$,$126 \times 10^{-4}$ and $280 \times 10^{-4}\,S\,m^2\,mol^{-1}$ respectively. Calculate $\Lambda _m^{\infty}$ for $Ba(OH)_2$ (in $S\,m^2\,mol^{-1}$).

Resistance of a conductivity cell (cell constant $129 \; m^{-1}$) filled with $74.5 \; ppm$ solution of $KCl$ is $100 \; \Omega$ (labelled as solution $1$). When the same cell is filled with $KCl$ solution of $149 \; ppm$,the resistance is $50 \; \Omega$ (labelled as solution $2$). The ratio of molar conductivity of solution $1$ and solution $2$ is i.e.,$\frac{\wedge_{1}}{\wedge_{2}} = x \times 10^{-3}$. The value of $x$ is (Nearest integer). Given,molar mass of $KCl$ is $74.5 \; g \; mol^{-1}$.

What is the value of $\Lambda _m^o$ $(NaCl)$ at $298 \ K$?