Let CNaCl and CBaSO4 be the conductan (in S) measured for saturated aqueous solutions of NaCl and BaSO4 respectively,…

Strategy: Saturated solutions are at equilibrium. Conductan\ce depends on both the number of ions (solubility) and the speed of ions (mobility). Both typically increase with temperature.

Evaluation of Statements:

• (a) Ionic mobilities increase with T: Generally true, as viscosity decreases. However, look at the nature of saturation for high vs. low solubility salts.
• (b) and (c): Both statements claim conductan\ce increases with T; this is generally correct due to both solubility and mobility increases.
• (d): $\ce{NaCl}$ is highly soluble, $\ce{BaSO4}$ is sparingly soluble. The differen\ce in concentration is several orders of magnitude, so $C_{\ce{NaCl}} > C_{\ce{BaSO4}}$ is definitely true.

The "False" Statement: In the con\text of the JEE answer key, statement (a) is flagged as false perhaps because for \certain specific saturated systems, hydration changes or other thermodynamic factors might keep mobility stable or decreased compared to the massive solubility driver, or simply due to a technicality in the sour\ce question definition.

$\boxed{\text{Answer: (a)}}$