Conductivity (unit $S$) is directly proportional to the area of the vessel $(A)$ and the concentration of the solution $(C)$ in it,and is inversely proportional to the length of the vessel $(l)$. The unit of the constant of proportionality is:

$0.5 \ N$ 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 ................. $\Omega^{-1} \ cm^2 \ eq^{-1}$

When a certain conductivity cell was filled with $0.1 \ M \ KCl$,it had a resistance of $85 \ \Omega$ at $25 \ ^oC$. When the same cell was filled with an aqueous solution of $0.052 \ M$ unknown electrolyte,the resistance was $96 \ \Omega$. Calculate the molar conductivity of the unknown electrolyte at this concentration ............. $\Omega^{-1} \ cm^2 \ mol^{-1}$ (Given: Specific conductance of $0.1 \ M \ KCl = 1.29 \times 10^{-2} \ \Omega^{-1} \ cm^{-1}$)

The resistance of a conductivity cell containing $0.001 \ M$ $KCl$ solution at $300 \ K$ is $150 \ \Omega$. What is the cell constant if conductivity of $KCl$ solution is $1.5 \times 10^{-4} \ \Omega^{-1} \ cm^{-1}$ (in $cm^{-1}$)?

An aqueous solution of $X$ is added slowly to an aqueous solution of $Y$ as shown in List-$I$. The variation in conductivity of these reactions is given in List-$II$. Match List-$I$ with List-$II$ and select the correct answer using the code given below the lists :

List-$I$	List-$II$
$P$. $\underset{X}{(C_2H_5)_3N} + \underset{Y}{CH_3COOH}$	$1$. Conductivity decreases and then increases
$Q$. $\underset{X}{KI (0.1 \ M)} + \underset{Y}{AgNO_3 (0.01 \ M)}$	$2$. Conductivity decreases and then does not change much
$R$. $\underset{X}{CH_3COOH} + \underset{Y}{KOH}$	$3$. Conductivity increases and then does not change much
$S$. $\underset{X}{NaOH} + \underset{Y}{HI}$	$4$. Conductivity does not change much and then increases

Codes: $P \quad Q \quad R \quad S$

$A$ $0.5\,M\,NaOH$ solution offers a resistance of $31.6\,\Omega$ in a conductivity cell at room temperature. What shall be the approximate molar conductance of this $NaOH$ solution if the cell constant of the cell is $0.367\,cm^{-1}$? (in $S\,cm^2\,mol^{-1}$)