The correct answer is A) Paithan.
The Satavahana dynasty was an Indian dynasty that ruled over the Deccan region from the 2nd century BCE to the 3rd century CE. The dynasty was founded by Simuka Satakarni, who is said to have overthrown the Mauryan Empire. The Satavahanas were a powerful dynasty that ruled over a large territory. They were patrons of art and literature, and their rule is considered to be a golden age in Indian history.
The Satavahana capital was located at Paithan, which is now a town in Maharashtra, India. Paithan was an important city during the Satavahana period, and it was a major center of trade and commerce. The city was also home to a number of important temples and monasteries.
The other options are incorrect. Amaravati was a Buddhist city that was located in Andhra Pradesh, India. Banavasi was a capital of the Kadambas, a dynasty that ruled over the Karnataka region. Hampi was a capital of the Vijayanagara Empire, which was a later dynasty that ruled over the Deccan region.