At $298 \ K$,the conductivity of $KCl$ solutions of molarity $0.1 \ M, 0.01 \ M$ and $1.0 \ M$ are recorded as $X, Y$ and $Z \ S \ cm^{-1}$ respectively. The correct relation between $X, Y$ and $Z$ is

Resistance of a conductivity cell filled with $0.1 \ mol \ L^{-1}$ $NaCl$ is $100 \ \Omega$. If the resistance of the same cell when filled with $0.02 \ mol \ L^{-1}$ $NaCl$ solution is $258 \ \Omega$,the conductivity of $0.02 \ mol \ L^{-1}$ $NaCl$ solution is (Conductivity of $0.1 \ mol \ L^{-1}$ $NaCl$ is $1.29 \ S \ m^{-1}$) (in $S \ m^{-1}$)

Molar conductivity of $0.01 \ M$ $HCl$ solution is $400.0 \ \Omega^{-1} \ cm^{2} \ mol^{-1}$. Calculate the conductivity of $HCl$ solution.

$0.5 \ N$ solution of a salt placed between two platinum electrodes $2.0 \ cm$ apart and of area of cross section $4.0 \ cm^2$ has a resistance of $25 \ \Omega$. Calculate the equivalent conductivity of solution ................. $\Omega^{-1} \ cm^2 \ eq^{-1}$

Solutions of two electrolytes $A$ and $B$ are diluted. The $\Lambda_m$ of $B$ increases $1.5$ times while that of $A$ increases $25$ times. Which of the two is a strong electrolyte? Justify your answer.

For a strong electrolyte, $\Lambda_{m}$ increases slowly with dilution and can be represented by the equation $\Lambda_{m} = \Lambda_{m}^{\circ} - Ac^{1/2}$. Molar conductivity values of a solution of strong electrolyte $AB$ at $18^{\circ} C$ are given below:

$c \ [mol \ L^{-1}]$	$0.04$	$0.09$	$0.16$	$0.25$
$\Lambda_{m} \ [S \ cm^2 \ mol^{-1}]$	$96.1$	$95.7$	$95.3$	$94.9$

The value of constant $A$ based on the above data [in $S \ cm^2 \ mol^{-1} / (mol \ L^{-1})^{1/2}$] is . . . . . . .