In the Group analysis of cations, $$Ba^{2+}$$ & $$Ca^{2+}$$ are precipitated respectively as

We need to identify how Ba²⁺ and Ca²⁺ are precipitated in group analysis of cations.

Group V cations include Ba²⁺, Ca²⁺, and Sr²⁺.

In the systematic qualitative analysis:

Ba²⁺ and Ca²⁺ both belong to Group V and are precipitated using ammonium carbonate ((NH₄)₂CO₃) as the group reagent.

Ba²⁺ → BaCO₃ (white precipitate)

Ca²⁺ → CaCO₃ (white precipitate)

Both are precipitated as carbonates.

Therefore, the answer is Option 4: carbonate & carbonate.