Variation of conductance of saturated aqueous solution with temperature

Question

The following question was asked in JEE Mains 2020:

Let $C_{\ce{NaCl}}$ and $C_{\ce{BaSO4}}$ be the conductances (in S) measured for saturated aqueous solutions of $\ce{NaCl}$ and $\ce{BaSO4}$, respectively, at a temperature $T$. Which of the following is false?

(A) Ionic mobilities of ions from both salts increase with $T$
(B) $C_{\ce{NaCl}} >> C_{\ce{BaSO4}}$ at a given $T$
(C) $C_{\ce{NaCl}}$($T_2$) > $C_{\ce{NaCl}}$($T_1$) for $T_2 > T_1$
(D) $C_{\ce{BaSO4}}$($T_2$) > $C_{\ce{BaSO4}}$($T_1$) for $T_2 > T_1$

My attempt:

(A) As temperature increases viscosity decreases leading to higher mobility, hence this is true.

(B) $\ce{BaSO4}$ is almost insoluble in water, hence its saturated solution will have a much smaller quantity of ions compared to an $\ce{NaCl}$ saturated solution, hence this is true.

(C) As can be seen from the graph here, the solublity of $\ce{NaCl}$ does increase with temperature, but only slightly; nevertheless this option is also true because it does increase and also ionic mobility increases.

(D) Dissolution of $\ce{BaSO4}$ is an endothermic process, hence I would expect solubility (hence conductance) to increase with temperature (although I was not able to find any data), therefore this option is also true.

Where am I going wrong? This is a single-correct question. The given answer is:

(A), but there are varied options found all over the web for this question

Answer 1

Okay, there is actually a trick way to solve the question. If any of A, C or D are false the one of the others also becomes false. (As mentioned by @AChem).
So the only option left is (B), which should (ideally) be the correct answer.

Now, coming to the actual reason, as per what I’ve found, conductivity ($k$) of salts in $aqueous$ solution depends on their concentration and number of ions generated on dissociation.

$k$ in aqueous solution or water : $Ba^{2+}$ > $Na^+$.
$k$ in molten state : $Ba^{2+}$ > $Na^+$.