Identifiy the correctly matched pair.

Calamine $ZnCO_3$

The correct answer is Option (3) → Calamine $ZnCO_3$.

Let us evaluate each option to determine the correct match between the ore and its chemical formula.

1. Bauxite [Al₂(OH)₄Si₂O₅]:

Incorrect. Bauxite is the primary ore of aluminum, but its formula is typically Al₂O₃ · xH₂O, not the given formula. The formula given here is incorrect and seems to describe a silicate compound, not bauxite.

2. Malachite Cu₂S:

Incorrect. Malachite is a copper ore, but its correct formula is Cu₂CO₃(OH)₂ (basic copper carbonate). The formula Cu₂S refers to chalcocite, another copper ore.

3. Calamine ZnCO₃:

Correct. Calamine is an ore of zinc, and its correct formula is ZnCO₃ (zinc carbonate). This is the correctly matched pair.

4. Cuprite CuFeS₂:

Incorrect. Cuprite is an oxide ore of copper, and its correct formula is Cu₂O. The formula CuFeS₂ corresponds to chalcopyrite, another copper ore.

Conclusion:

The correct pair is Calamine ZnCO₃.