At 300 K , the molar conductivities of the aqueous solutions of three salts at two different concentrations are given below :

Salt	Concentration (M)	Molar conductivity (S cm2 mol−1)
NaNO3	0.01	111
	0.04	101
NaCl	0.01	117
	0.04	107
AgNO3	0.01	125
	0.04	116

The conductivity of a saturated aqueous solution of AgCl is $1.40 \times 10^{-6} \mathrm{~S} \mathrm{~cm}^{-1}$ at 300 K . If the solubility of AgCl in water at 300 K is $\boldsymbol{X} \mathrm{mol} \mathrm{L}^{-1}$, then $\log _{10}\left(\boldsymbol{X}^{-1}\right)$ is

(Assume that AgCl dissolved in water ionizes completely and that the molar conductivity of saturated AgCl solution is equal to its limiting molar conductivity.)

In a conductometric titration, small volume of titrant of higher concentration is added stepwise to a larger volume of titrate of much lower concentration, and the conductance is measured after each addition.

The limiting ionic conductivity $\left(\Lambda_0\right)$ values (in $\mathrm{mS} \mathrm{m}{ }^2 \mathrm{~mol}^{-1}$ ) for different ions in aqueous solutions are given below:

$$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline \text { Ions } & \mathrm{Ag}^{+} & \mathrm{K}^{+} & \mathrm{Na}^{+} & \mathrm{H}^{+} & \mathrm{NO}_3^{-} & \mathrm{Cl}^{-} & \mathrm{SO}_4^{2-} & \mathrm{OH}^{-} & \mathrm{CH}_3 \mathrm{COO}^{-} \\ \hline \Lambda_0 & 6.2 & 7.4 & 5.0 & 35.0 & 7.2 & 7.6 & 16.0 & 19.9 & 4.1 \\ \hline \end{array} $$

For different combinations of titrates and titrants given in List-I, the graphs of 'conductance' versus 'volume of titrant' are given in List-II.

Match each entry in List-I with the appropriate entry in List-II and choose the correct option.

LIST-I	LIST-II
(P) Titrate: KCl Titrant: AgNO$_3$
(Q) Titrate: AgNO$_3$ Titrant: KCl
(R) Titrate: NaOH Titrant: HCl
(S) Titrate: NaOH Titrant: CH$_3$COOH

Plotting $1 / \Lambda_{\mathrm{m}}$ against $\mathrm{c} \Lambda_{\mathrm{m}}$ for aqueous solutions of a monobasic weak acid $(\mathrm{HX})$ resulted in a straight line with $\mathrm{y}$-axis intercept of $\mathrm{P}$ and slope of $\mathrm{S}$. The ratio $\mathrm{P} / \mathrm{S}$ is

$$ \begin{aligned} & {\left[\Lambda_{\mathrm{m}}=\right.\text { molar conductivity }} \\\\ & \Lambda_{\mathrm{m}}^{\mathrm{o}}=\text { limiting molar conductivity } \\\\ & \mathrm{c}=\text { molar concentration } \\\\ & \left.\mathrm{K}_{\mathrm{a}}=\text { dissociation constant of } \mathrm{HX}\right] \end{aligned} $$

Molar conductivity ($$\Lambda $$_m) of aqueous solution of sodium stearate, which behaves as a strong electrolyte, is recorded at varying concentrations (C) of sodium stearate. Which one of the following plots provides the correct representation of micelle formation in the solution?

(critical micelle concentration (CMC) is marked with an arrow in the figures)