The correct answer is option 1 - Gulbarga. The Bahamani Kings established their capital in Gulbarga, which is located in present-day Karnataka, India. Gulbarga was chosen as the capital because of its strategic location, serving as a center for trade, commerce, and administration. The Bahamani Kingdom, also known as the Bahmani Sultanate, was a Muslim state that ruled over parts of the Deccan region in South India from the 14th to the 16th century. It was during this time that Gulbarga flourished and became an important cultural and political center. The rule of the Bahamani Kings was marked by the construction of notable architectural structures, including mosques, palaces, and tombs, which can still be seen in Gulbarga today.