Background:
Bahadur Shah was the Mughal emperor who ruled from 1707 to 1712. During his reign, the Marathas under the leadership of Shivaji and later his descendants, expanded their influence in the Deccan region. The Marathas demanded certain concessions from the Mughal emperor, including the collection of chauth (a tax of one-fourth of the revenue) and sardeshmukhi (an additional tax of 10% on the revenue) in the Deccan territories.

Explanation:
During Bahadur Shah's rule, he granted several concessions to the Marathas in the Deccan region to maintain their support and loyalty. However, one of the concessions that were not granted to the Marathas was the control over Berar.

Chauth:
- Bahadur Shah granted the Marathas the right to collect chauth, which was a tax of one-fourth of the revenue, from the Deccan territories.
- This gave the Marathas a significant source of income and allowed them to expand their military and political influence in the region.

Sardeshmukhi:
- In addition to chauth, Bahadur Shah also granted the Marathas the right to collect sardeshmukhi, which was an additional tax of 10% on the revenue, from the Deccan territories.
- This further increased the Marathas' revenue and strengthened their position in the Deccan.

Control over Berar:
- Berar was a prosperous region in the Deccan, known for its fertile lands and rich resources.
- The Marathas had been vying for control over Berar, as it would have provided them with additional revenue and territorial expansion.
- However, Bahadur Shah did not grant the Marathas the control over Berar, which remained under Mughal control.

Conclusion:
In conclusion, Bahadur Shah granted the Marathas the right to collect chauth and sardeshmukhi in the Deccan territories, which significantly increased their revenue and power. However, he did not grant them the control over Berar, which remained under Mughal control. Therefore, the correct answer is option 'A' - Chauth was not granted to the Marathas in the Deccan by Bahadur Shah.

A