Consider the statements $S_1$ and $S_2$:
$S_1$: Conductivity always increases with decrease in the concentration of electrolyte.
$S_2$: Molar conductivity always increases with decrease in the concentration of electrolyte.
The correct option among the following is

The property which decreases with dilution is:

Which one of the following solutions will have the highest conductivity?

The specific conductance of $0.0025 \ M$ acetic acid is $5 \times 10^{-5} \ S \ cm^{-1}$ at a certain temperature. The dissociation constant of acetic acid is $...... \times 10^{-7}$. (Nearest integer) Consider limiting molar conductivity of $CH_3COOH$ as $400 \ S \ cm^2 \ mol^{-1}$.

The following figure shows the dependence of molar conductance of two electrolytes on concentration. $\Lambda_m^0$ is the limiting molar conductivity. The number of incorrect statement$(s)$ from the following is $...........$
$(A)$ $\Lambda_m^0$ for electrolyte $A$ is obtained by extrapolation.
$(B)$ For electrolyte $B$,the $\Lambda_m$ vs $\sqrt{c}$ graph is a straight line with an intercept equal to $\Lambda_m^0$.
$(C)$ At infinite dilution,the value of the degree of dissociation approaches zero for electrolyte $B$.
$(D)$ $\Lambda_m^0$ for any electrolyte $A$ or $B$ can be calculated using $\lambda^0$ for individual ions.

The limiting molar conductivities of $NaI$,$NaNO_3$ and $AgNO_3$ are $12.7$,$12.0$ and $13.3 \, mS \, m^2 \, mol^{-1}$,respectively (all at $25^{\circ} C$). The limiting molar conductivity of $AgI$ at this temperature is $.... \, mS \, m^2 \, mol^{-1}$.