Which of the following is the correct relationship between molar conductivity $(\Lambda_m)$,conductivity $(k)$,and molarity $(M)$ of a solution for an electrolyte?

Molar conductivities at infinite dilution $\wedge_{m}^{\circ}$ for $Ba(OH)_2$,$BaCl_2$ and $NH_4Cl$ are $457.0$,$240.6$ and $213.0 \ S \ cm^2 \ mol^{-1}$ respectively. The $\wedge_{m}^{\circ}$ for ammonium hydroxide (in $S \ cm^2 \ mol^{-1}$) is (in $.2$)

Calculate $\Lambda _m^o$ for $CaCl_2$ and $MgSO_4$ from the data given in the table below:

Ion and $\lambda ^o / (S \ cm^2 \ mol^{-1})$	Ion and $\lambda ^o / (S \ cm^2 \ mol^{-1})$
$H^{+} : 349.6$	$OH^{-} : 199.1$
$Na^{+} : 50.1$	$Cl^{-} : 76.3$
$K^{+} : 73.5$	$Br^{-} : 78.1$
$Ca^{2+} : 119.0$	$CH_3COO^{-} : 40.9$
$Mg^{2+} : 106.0$	$SO_4^{2-} : 160.0$

Resistance of a cell containing $0.02 \ M \ KCl$ solution is $164 \ \Omega$. If the cell is filled with $0.05 \ M \ AgNO_3$,the resistance becomes $75.8 \ \Omega$. Calculate the following: [Conductivity of $0.02 \ M \ KCl = 2.768 \times 10^{-3} \ \Omega^{-1} \ cm^{-1}$] $(i)$ Conductivity of $0.05 \ M \ AgNO_3$ (ii) Molar conductivity of $AgNO_3$ solution.

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:

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