The archaeological site containing important Buddhist ruins:

Hampi
Badami
Aihole
Sannati

The correct answer is D) Sannati.

Sannati is an archaeological site in the Gulbarga district of Karnataka, India. It is located on the banks of the Malaprabha River, about 100 kilometers from the city of Gulbarga. The site is known for its Buddhist ruins, which date back to the 2nd century BCE. The ruins include stupas, monasteries, and temples.

Badami, Aihole, and Hampi are also important archaeological sites in Karnataka. Badami is a UNESCO World Heritage Site that is known for its cave temples, which were built by the Chalukya dynasty in the 6th century CE. Aihole is a smaller site that is also known for its cave temples. Hampi is a UNESCO World Heritage Site that was the capital of the Vijayanagara Empire in the 16th century CE. It is known for its temples, palaces, and other monuments.

Sannati is a lesser-known archaeological site, but it is no less important. The Buddhist ruins at Sannati are some of the oldest in India. They provide valuable insights into the history of Buddhism in India. The site is also a beautiful place to visit, with its ancient temples and monasteries set against the backdrop of the Malaprabha River.