This checks a fact from medieval Indian history about the founding of the Bahmani Sultanate.
Mahmud Gawan Bahmani: Mahmud Gawan was a famous and capable prime minister of the Bahmani Kingdom decades later, not its founder.
Mohammad Yusuf Bahmani: this name does not correspond to the founder of the Bahmani Kingdom.
Hasan Gangu Bahmani: correct. In 1347, Hasan Gangu, an Afghan officer who had served under Muhammad bin Tughlaq, revolted and set up the independent Bahmani Kingdom in the Deccan, taking the title Ala-ud-din Bahman Shah.
Khwaja Tuglak Bahmani: this name is not linked to the founding of the Bahmani Kingdom.
The correct option is C, Hasan Gangu Bahmani, founder of the Bahmani Kingdom in 1347.