Step 1: Background of the Chronicle:
The Ain-i-Akbari (meaning “Administration/Institutes of Akbar”) is a highly detailed $16^{\text{th}}$-century document that records the imperial administration, army, statistics, geography, and diverse religious and cultural traditions of the Mughal Empire during Akbar's reign.
Step 2: Identifying the Author:
The book was written by Akbar's close friend, vizier, and court historian, Abu'l Fazl ibn Mubarak. It forms the third volume of his larger, monumental official history of Akbar's reign, the Akbarma.
Step 3: Checking Other Options:
• Iyat Khan (A): Wrote the Shahjahanma (history of Shah Jahan's reign).
• Abdul Hamid Lahori (C): Authored the Padshahma (history of Shah Jahan's reign).
• Abdul Qadir Badayuni (D): A contemporary historian who wrote Muntakhab-ut-Tawarikh, often criticizing Akbar's liberal religious policies.
Step 4: Conclusion:
The author of the *Ain-i-Akbari* is Abu'l Fazl, corresponding to option (B).