Detailed Explanation:

Ain-i-Akbari was written by Abul Fazl, one of the Navratnas (Nine Jewels) in Emperor Akbar's court. It is the third volume of the Akbarnama and provides a detailed administrative, social, and statistical account of Akbar's empire compiled between 1590–1596.

Abdul Qadir Badauni wrote Muntakhab-ut-Tawarikh, and Khwaja Nizamuddin Ahmad authored Tabaqat-i-Akbari—both different historical works from the Mughal period.

Therefore, Abul Fazl authored Ain-i-Akbari, making Option 4 the correct answer.