Variation of conductance of saturated aqueous solution with temperature

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](https://chemistry.stackexchange.com/a/69047/24750), 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
> 
> 
> 




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 : $Ba^{2+}$ > $Na^+$.


 0