Option a is the correct answer. The capital of Chalukyas was Vatapi or Badami, which is located in the modern state of Karnataka. The Chalukyas were a powerful dynasty that ruled over large parts of southern and central India from the 6th to the 12th centuries. They had different branches and capitals, such as the Eastern Chalukyas of Vengi and the Western Chalukyas of Kalyani. Aihole, another city in Karnataka, was the first capital of the Chalukyas and is known as the birthplace of Indian architecture