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The correct answer is option 2: 1 and 3 only.
Let`s break down each statement:
Statement 1: Akbar Nama and Badshah Nama are the important illustrated Mughal official histories.
This statement is correct. Both Akbar Nama and Badshah Nama are significant works that document the history of the Mughal Empire.
Statement 2: While Akbar Nama was written by Abdul Hamid Lahori, Badshah Nama was authored by Abu`l Fazl.
This statement is incorrect. The authors of these works are actually the opposite. Akbar Nama was written by Abu`l Fazl, whereas Badshah Nama was authored by Abdul Hamid Lahori.
Statement 3: The Akbar Nama is divided into three books, of which the third book is the Ain-i-Akbari.
This statement is correct. The Akbar Nama is indeed divided into three books, and the third book is known as Ain-i-Akbari. The Ain-i-Akbari is a detailed record that provides information on the administration, revenues, and economy of the Mughal Empire during Akbar`s reign.
Therefore, the correct statements are