What is the mathematical relationship between the radius $(r)$ of a cylindrical conductor and its cross-sectional area $(A)$?

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

Let $C_{NaCl}$ and $C_{BaSO_4}$ be the conductances (in $S$) measured for saturated aqueous solutions of $NaCl$ and $BaSO_4,$ respectively,at a temperature $T.$ Which of the following is false?

The specific conductivities (in $\Omega^{-1} \text{ cm}^{-1}$) of four electrolytes $P, Q, R,$ and $S$ are given in the brackets. Which one offers the maximum resistance when current is passed through them?
$P (5.0 \times 10^{-5}), Q (7.0 \times 10^{-8}), R (1.0 \times 10^{-10}), S (9.2 \times 10^{-3})$

The conductance of a $0.0015 \ M$ aqueous solution of a weak monobasic acid was determined by using a conductivity cell consisting of platinized $Pt$ electrodes. The distance between the electrodes is $120 \ cm$ with an area of cross section of $1 \ cm^2$. The conductance of this solution was found to be $5 \times 10^{-7} \ S$. The $pH$ of the solution is $4$. The value of limiting molar conductivity $\left(\Lambda_{m}^0\right)$ of this weak monobasic acid in aqueous solution is $Z \times 10^2 \ S \ cm^{2} \ mol^{-1}$. The value of $Z$ is

What must be the molarity of $BaCl_2$ solution to have molar conductivity $240 \text{ }\Omega^{-1}\text{cm}^2\text{mol}^{-1}$ and conductivity $0.012 \text{ }\Omega^{-1}\text{cm}^{-1}$ at $25 \text{ }^\circ\text{C}$ (in M)?