The Satavahanas, a powerful dynasty that ruled over much of the Deccan, including parts of Andhra Pradesh, had their capital at:

Amaravati
Nagarjunakonda
Paithan (Pratishthana)
Kondapur

The correct answer is: c) Paithan (Pratishthana).

The Satavahanas were a powerful dynasty that ruled over much of the Deccan, including parts of Andhra Pradesh, from the 2nd century BCE to the 3rd century CE. Their capital was at Paithan (Pratishthana), which is now in the Aurangabad district of Maharashtra. Paithan was an important city during the Satavahana period, and it was a major center of trade and commerce. It was also a center of learning and culture. The Satavahanas were patrons of the arts and sciences, and they built many temples, palaces, and other monuments at Paithan.

Amaravati was an important city during the Satavahana period, but it was not their capital. It was a major center of Buddhist learning and culture. Nagarjunakonda was also an important city during the Satavahana period, but it was not their capital. It was a major center of Buddhist learning and culture. Kondapur was a minor city during the Satavahana period, and it was not their capital.