According to some traditions, Pampadevi, the local mother goddess, did penance in the rocky hills located on the banks of river Tungabhadra for which of the following diety?

Virupaksha

The correct answer is Option 2 - Virupaksha

According to local tradition, the rocky hills on the banks of the Tungabhadra river sheltered the monkey kingdom of Vali and Sugriva mentioned in the Ramayana. Other traditions suggest that Pampadevi, the local mother goddess, did penance in these hills in order to marry Virupaksha, the guardian deity of the kingdom, also recognised as a form of Shiva. To this day this marriage is celebrated annually in the Virupaksha temple. Among these hills are found Jaina temples of the pre-Vijayanagara period as well. In other words, this area was associated with several sacred traditions.