The Bahmani kingdom was founded by Alauddin Hasan. Option 1, Ahmad Shah I, is incorrect. Option 3, Mahmud Gavan, is incorrect. Option 4, Firuz Shah Bahmani, is incorrect. The Bahmani kingdom was established in 1347 by Alauddin Hasan, who took the title of Sultan Alauddin Bahman Shah. He was a nobleman from the Delhi Sultanate and rebelled against the rule of Muhammad bin Tughluq. Alauddin Hasan established his own kingdom, which came to be known as the Bahmani kingdom, with its capital in Gulbarga (in present-day Karnataka, India). It was one of the major medieval Deccan Sultanates and lasted for nearly two and a half centuries, until it was eventually conquered by the Mughal Empire.