The district famous for the Hampi ruins:

Ballari
Raichur
Koppal
Vijayapura

The correct answer is: A) Ballari.

Hampi is a UNESCO World Heritage Site located in the Ballari district of Karnataka, India. It was the capital of the Vijayanagara Empire from 1336 to 1565. The ruins of Hampi are spread over an area of 4,000 hectares and are a major tourist attraction.

The other options are incorrect because:

  • Raichur is a district in the northern part of Karnataka. It is not famous for the Hampi ruins.
  • Koppal is a district in the northern part of Karnataka. It is not famous for the Hampi ruins.
  • Vijayapura is a district in the northern part of Karnataka. It is not famous for the Hampi ruins.