Barium sulfate conducts electricity only in the molten state since when in solid form the ions (Ba+ & SO²4) are in fixed positions. When melted, these ions become mobile and hence can conduct electricity.
The other compounds provided i.e.
A. sodium bromide
B. calcium hydroxide and
D. magnesium sulfate,
are soluble hence can conduct electricity both in molten state and solution.
Thus the correct answer is:
C. barium sulfate