In the wet tests for detection of various cations by precipitation, Ba$$^{2+}$$ cations are detected by obtaining precipitate of

In the wet test (qualitative analysis), Ba²⁺ cations belong to Group V (alkaline earth metals).

Ba²⁺ is detected by precipitation as barium carbonate (BaCO₃) using ammonium carbonate as the group reagent:

$$Ba^{2+} + (NH_4)_2CO_3 \to BaCO_3 \downarrow + 2NH_4^+$$

BaCO₃ is a white precipitate.

Note: While BaSO₄ is also an insoluble precipitate, in the systematic qualitative analysis scheme, Ba²⁺ is detected using carbonate precipitation in Group V analysis.

This matches option 2: BaCO₃.