What is the name of the book authored by Abul Fazl? 

Ain-i Akbari 

The correct answer is Option 2 - Ain-i Akbari

Ain-i Akbari was authored by Abul Fazl.

The Ain-i Akbari was the culmination of a large historical, administrative project of classification undertaken by Abu’l Fazl at the order of Emperor Akbar. It was completed in 1598, the forty-second regnal year of the emperor, after having gone through five revisions. The Ain was part of a larger project of history writing commissioned by Akbar.