Answer
See answer below.
Work Step by Step
a) $BaCl_2(aq)+Na_2SO_4(aq)\rightarrow BaSO_4(s)+2\ NaCl$
Any combination including a barium cation and a sulfate ion would fit the criteria, except barium carbonate with sulfuric acid.
b)$BaCO_3(s)+H_2SO_4(aq)\rightarrow BaSO_4(s)+H_2O(l)+CO_2(g)$
This is the only valid option.