Explanation:

- Eastern Chalukyas: They were a South Indian dynasty, and their capital city during a certain period was called Vengi.

- Option 1: Peddavegi: Located in Andhra Pradesh, this site is often associated with the ancient city of Vengi. It was the administrative center of the Eastern Chalukyas, known for its historical significance and archaeological findings.

- Option 2: Erumaiyur: This place does not have historical associations or recognition connected to the Eastern Chalukyas.

- Option 3: Salihundam: primarily known as a Buddhist heritage site, it has no historical links to being the capital of the Eastern Chalukyas.

- Option 4: Bhattiprolu: This is an ancient Buddhist site known for inscriptions in Brahmi script, not related to Eastern Chalukya’s capital.

- Correct Answer: Option 1 (Peddavegi): This is the historically acknowledged site corresponding to the ancient capital city Vengi of the Eastern Chalukyas.