An inscription records that a king repaired an old temple and granted…

The correct answer is Option (1) → To win support and recognition for the king's power, wealth and piety

Option (1) To win support and recognition for the king's power, wealth and piety — Correct. Rulers built, repaired and maintained temples and granted them land. These acts were means of winning support and recognition for their power, wealth and piety, so a repair and a village grant fit this aim.

Option (2) To place the temple lands under the amara-nayakas for collecting revenue — Incorrect. Amara-nayakas were military chiefs who collected taxes from territories the king gave them. A village granted to a temple went to the temple's own upkeep and stayed with it.

Option (3) To mark the boundary between the sacred centre and the royal centre — Incorrect. The sacred centre and the royal centre were zones of the city itself. A repair with a village grant was a religious gift and does not mark any such line.

Option (4) To convert an old Jaina shrine into a shrine of the god Virupaksha — Incorrect. Jaina temples of the pre-Vijayanagara period did stand among these hills. Repairing and endowing a temple served the king's own standing and had nothing to do with changing a shrine's deity.