Introduction:
Nizam-ul-Mulk played a significant role in the overthrow of the Saiyyid brothers and was rewarded with the viceroyalty of Deccan by Muhammad Shah. This answer will explain the context, events, and reasons behind Nizam-ul-Mulk's reward.

Context:
During the early 18th century, the Mughal Empire faced considerable political instability and regional fragmentation. The decline of central authority led to the rise of powerful regional states and local rulers. In this context, the Saiyyid brothers, Abdullah Khan and Hussain Ali Khan, emerged as influential figures in the Mughal court.

Overthrow of the Saiyyid Brothers:
Nizam-ul-Mulk, whose actual name was Asaf Jah, served as the governor of Malwa under the Saiyyid brothers. However, he grew unhappy with their misrule and decided to join forces with other discontented nobles to overthrow them. In 1720, Nizam-ul-Mulk, supported by the Marathas, successfully defeated the Saiyyid brothers and captured Delhi.

Reasons for Reward:
1. Contribution to the Overthrow: Nizam-ul-Mulk played a leading role in the overthrow of the Saiyyid brothers. His military and political skills were crucial in ensuring their defeat. By removing a corrupt and ineffective regime, Nizam-ul-Mulk helped stabilize the Mughal Empire.

2. Strengthening Imperial Authority: Muhammad Shah, the Mughal emperor at that time, recognized the importance of having loyal and capable administrators in the provinces. Nizam-ul-Mulk's success in removing the Saiyyid brothers and establishing control over Deccan demonstrated his loyalty and effectiveness. By rewarding him with the viceroyalty, Muhammad Shah aimed to strengthen the imperial authority in the region.

3. Administrative Capability: Nizam-ul-Mulk was known for his administrative skills and ability to govern effectively. His appointment as the viceroy of Deccan was a strategic move to ensure efficient administration and revenue collection in that region. Muhammad Shah trusted Nizam-ul-Mulk to bring stability and prosperity to Deccan.

4. Maratha Alliance: The Marathas had supported Nizam-ul-Mulk in his campaign against the Saiyyid brothers. The Marathas were a powerful regional force and had a significant influence in the Deccan. By rewarding Nizam-ul-Mulk, Muhammad Shah also aimed to maintain a favorable relationship with the Marathas and secure their support in the future.

Conclusion:
In conclusion, Nizam-ul-Mulk's leading role in the overthrow of the Saiyyid brothers earned him the reward of the viceroyalty of Deccan by Muhammad Shah. His contributions to removing a corrupt regime, his administrative capabilities, and the support of the Marathas were key factors that led to this reward. This appointment aimed to strengthen imperial authority, ensure efficient governance, and maintain alliances in the region.

A. Muhammad Shah