During Akbar's reign, the Mughal Empire expanded its territories into the Deccan region of India. Several provinces were established in the Deccan, but one of them was not a Mughal province during Akbar's reign. Let's analyze each option to understand why:

a) Berar: Berar was a Mughal province in the Deccan during Akbar's reign. It was located in present-day Maharashtra and was established as a province in 1596. Akbar appointed Mirza Aziz Koka as the governor of Berar.

b) Bidar: Bidar was not a Mughal province in the Deccan during Akbar's reign. Bidar was the capital of the Bahmani Sultanate, which was established in the 14th century. The Mughals did not conquer Bidar during Akbar's reign, and it remained under the control of the Bahmani Sultanate until it was annexed by the Nizam of Hyderabad in the 17th century.

c) Ahmadnagar: Ahmadnagar was a Mughal province in the Deccan during Akbar's reign. It was located in present-day Maharashtra and was annexed by the Mughals in 1595. Akbar appointed Mirza Aziz Koka as the governor of Ahmadnagar.

d) Khandesh: Khandesh was a Mughal province in the Deccan during Akbar's reign. It was located in present-day Maharashtra and was annexed by the Mughals in 1601. Akbar appointed Khan Jahan Quli as the governor of Khandesh.

Therefore, the correct answer is option 'B' - Bidar. Bidar was not a Mughal province in the Deccan during Akbar's reign.