The conductivity of a solution containing $2.08 \ g$ of anhydrous barium chloride in $200 \ mL$ solution is $6 \times 10^{-3} \ \Omega^{-1} \ cm^{-1}$. The molar conductivity of the solution (in $\Omega^{-1} \ cm^2 \ mol^{-1}$) is $\underline{x} \times 10^2$. The value of $\underline{x}$ is (Atomic mass of $Ba=137, Cl=35.5$)

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

What is the conductivity of $0.05 \ M$ $KCl$ solution if cell constant is $1.32 \ cm^{-1}$ and resistance is $528 \ \Omega$?

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)?

The molar conductivity of $0.02 \ M$ $AgI$ at $298 \ K$ is $142.3 \ \Omega^{-1} \ cm^2 \ mol^{-1}$. What is its conductivity?

Given below are two statements :
Statement $I :$ The limiting molar conductivity of $KCl$ (strong electrolyte) is higher compared to that of $CH_{3}COOH$ (weak electrolyte).
Statement $II :$ Molar conductivity decreases with decrease in concentration of electrolyte.
In the light of the above statements,choose the most appropriate answer from the options given below: