Step 1: Understanding the context.
Akbar, the Mughal emperor, ruled from 1556 to 1605. During his reign, several historians wrote about his rule. One of the prominent historians of Akbar’s court was Badauni, who is known for his historical writings, particularly his work "Muntakhab-ut-Tawarikh."
Step 2: Analyzing the options.
(A) Farishta: Farishta, a Persian historian, was not a contemporary of Akbar but wrote about his reign later.
(B) Badauni: Correct. Badauni was a contemporary historian of Akbar and wrote extensively about his rule.
(C) Mulla Daud: Mulla Daud was a notable figure, but he did not write as a contemporary of Akbar.
(D) Ibn Battuta: Ibn Battuta, the famous traveler and historian, visited India long before Akbar’s time.
Step 3: Conclusion.
The correct answer is (B) Badauni, as he was a contemporary historian during Akbar’s reign.