Which of the following statements is correct?

The correct answer is Option (1) → Oxidation occurs at the anode in both galvanic and electrolytic cells.

The electrodes are named by the reaction at them: the anode is where oxidation takes place and the cathode is where reduction takes place. This holds for both kinds of cell.

Why the other options are incorrect

Option (2) Reduction occurs at the anode in an electrolytic cell, whereas oxidation occurs at the cathode in a galvanic cell. — Incorrect. Both halves are reversed: the anode of an electrolytic cell is the site of oxidation, and the cathode of a galvanic cell is the site of reduction.

Option (3) Reduction occurs at the anode in both galvanic and electrolytic cells. — Incorrect. Reduction always takes place at the cathode, in both cells.

Option (4) Oxidation occurs at the anode in an electrolytic cell, whereas reduction occurs at the anode in a galvanic cell. — Incorrect. The first half is right, but the anode of a galvanic cell is also the site of oxidation, as when zinc dissolves in the Daniell cell.

NCERT (2026-27 edition):
2.2 Galvanic Cells – “… In a galvanic cell, the half-cell in which oxidation takes place is called anode and it has a negative potential with respect to the solution.”

2.5 Electrolytic Cells and Electrolysis – “In an electrolytic cell external source of voltage is used to bring about a chemical reaction. … Thus copper is dissolved (oxidised) at anode and deposited (reduced) at cathode.”