‘Adhai Din Ka Jhopra’ or ‘A hut of two and a half days’ at Ajmer was built by Qutbuddin Aibak. The monument is located in Ajmer, Rajasthan, India and was constructed in 1199 CE. It is an important example of Indo-Islamic architecture and is considered as one of the earliest surviving Islamic structures in India.

Qutbuddin Aibak was a prominent military commander and the first Sultan of Delhi from the Mamluk dynasty. He also initiated the construction of the Qutub Minar in Delhi. Although he ruled for a short period, his architectural contributions left a significant impact on the history of Indian architecture.

Option 2, Balban, is incorrect as he succeeded Qutbuddin Aibak and ruled after him. Option 3, Alauddin Khalji, and option 4, Muhammad-bin-Tughlaq, are also incorrect as they ruled many years after the construction of ‘Adhai Din Ka Jhopra’.