If the resistance of a $0.01 \, M$ electrolyte in a cell is $40 \, \Omega$ and the cell constant is $0.4 \, \text{cm}^{-1}$,what is the molar conductivity in $\Omega^{-1} \, \text{cm}^2 \, \text{mol}^{-1}$?

At a certain temperature and at infinite dilution,the equivalent conductances of sodium benzoate,hydrochloric acid,and sodium chloride are $240$,$349$,and $229 \ \Omega^{-1} \ cm^2 \ equiv^{-1}$ respectively. The equivalent conductance of benzoic acid in $\Omega^{-1} \ cm^2 \ equiv^{-1}$ at the same conditions is

Resistance of a decimolar solution between two electrodes $0.02 \ m$ apart and $0.0004 \ m^2$ in area was found to be $50 \ \Omega$. Specific conductance $(\kappa)$ is $:$

Conductivity of a saturated solution of a sparingly soluble salt $AB$ at $298 \ K$ is $1.85 \times 10^{-5} \ S \ m^{-1}$. Solubility product of the salt $AB$ at $298 \ K$ is. Given $\Lambda_{m}^{\circ}(AB) = 140 \times 10^{-4} \ S \ m^{2} \ mol^{-1}$.

The limiting molar conductivities of the given electrolytes at $298 \ K$ follow the order: $\lambda^{\circ}_{(K^{+})} = 73.5, \lambda^{\circ}_{(Cl^{-})} = 76.3, \lambda^{\circ}_{(Ca^{2+})} = 119.0, \lambda^{\circ}_{(SO_{4}^{2-})} = 160.0 \ S \ cm^{2} \ mol^{-1}$.

The resistance of $0.01 \ N$ $NaCl$ solution at $25 \ ^oC$ is $200 \ \Omega$. The cell constant of the conductivity cell is $1 \ cm^{-1}$. The equivalent conductance is: