The correct answer is: a) Pulakesin I.
Pulakesin I was the founder of the Eastern Chalukya dynasty in 610 CE. He was a powerful ruler who expanded his kingdom to include much of the Deccan Plateau. He was also a patron of the arts and literature.
Pulakesin I was born in 590 CE in the town of Vatapi, which is now known as Badami. He was the son of the Chalukya king Kirtivarman I. Pulakesin I succeeded his father to the throne in 610 CE.
Pulakesin I was a skilled military leader. He defeated the Pallavas, the Rashtrakutas, and the Kadambas. He also expanded his kingdom to include much of the Deccan Plateau.
Pulakesin I was a patron of the arts and literature. He built many temples and monasteries. He also supported the work of many poets and scholars.
Pulakesin I died in 642 CE. He was succeeded by his son, Vikramaditya I.
The other options are incorrect.
Option b) Vishnuvardhana was the founder of the Western Chalukya dynasty.
Option c) Rajaraja Chola I was the founder of the Chola dynasty.
Option d) Vikramaditya I was the son of Pulakesin I and the successor to his throne.