Dhanyakataka, a significant Buddhist Centre under the Mahasanghikas, was indeed located in Andhra Pradesh, which is why Option 1 is the correct answer. Here`s a breakdown of the options:

Option 1 - Andhra: This is the correct option; Dhanyakataka was located in present day Guntur district in Andhra Pradesh. It was an important center for Buddhism, and the historic site is also famous for the Great Stupa.

Option 2 - Gandhara: Incorrect. Gandhara was an ancient region, presently in today’s northern Pakistan. It flourished as a great center of Greco-Buddhist art, but wasn`t where Dhanyakataka was located.

Option 3 - Kalinga: Incorrect. Kalinga, presently in Odisha, also has a rich Buddhist history, but Dhanyakataka was not located there.

Option 4 - Magadha: Incorrect. Magadha in Bihar was indeed the centre of many ancient kingdoms. But it is not connected with Dhanyakataka. Dhanyakataka thrived in Andhra, not Magadha.