The correct answer is Option 1- Pratishthana

The capital of the Satavahana Dynasty was Paithan (Prathisthana). It is located on the banks of the Godavari River in present-day Maharashtra, India. Paithan was founded by the Satavahana king Simuka in the 2nd century BCE. It was a major center of trade and commerce, and it was also home to a number of important temples and other religious sites.

The Satavahanas ruled over a large territory that included much of present-day India, from the Vindhya Mountains in the north to the Krishna River in the south. Their capital, Paithan, was a major center of political and cultural power.

The other options are incorrect. Vidisha was the capital of the Avanti kingdom, which was a rival of the Satavahanas. Patliputra was the capital of the Maurya Empire, which preceded the Satavahanas. Vanji was the capital of the Chera dynasty, which was a contemporary of the Satavahanas.