$A$ conductivity cell containing $5 \times 10^{-4} \ M \ NaCl$ solution develops a resistance of $14000 \ \Omega$ at $25^{\circ} C$. Calculate the conductivity of the solution if the cell constant is $0.84 \ cm^{-1}$.

For a saturated solution of $CaF_2$,choose the correct relationship-

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 $\Lambda_{m}^{\circ}(AB) = 140 \times 10^{-4} \ S \ m^{2} \ mol^{-1}$.

Calculate $\wedge_0$ of $CH_2ClCOOH$ if $\wedge_0$ for $HCl, KCl$ and $CH_2ClCOOK$ are $4.2, 1.5$ and $1.1 \ \Omega^{-1} \ cm^2 \ mol^{-1}$ respectively.

The number of correct statements from the following is $...........$.
$(A)$ Conductivity always decreases with decrease in concentration for both strong and weak electrolytes.
$(B)$ The number of ions per unit volume that carry current in a solution increases on dilution.
$(C)$ Molar conductivity increases with decrease in concentration.
$(D)$ The variation in molar conductivity is different for strong and weak electrolytes.
$(E)$ For weak electrolytes,the change in molar conductivity with dilution is due to decrease in degree of dissociation.

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