The Carnatic was one of the subahs (provinces) of the Mughal Deccan. It came under the authority of the Nizam of Hyderabad.

Explanation:
The Carnatic region was a significant province in the Deccan during the Mughal period. It encompassed the present-day states of Tamil Nadu, Andhra Pradesh, and parts of Karnataka and Kerala. The Mughal Empire divided its territories into subahs, which were administrative divisions ruled by subahdars or governors. The Nizam of Hyderabad was appointed as the subahdar of the Carnatic region.

The Nizam of Hyderabad:
- The Nizam of Hyderabad was a title used by the monarchs of the Hyderabad State, which was an independent state in southern India.
- The Nizam held substantial power and was considered one of the wealthiest rulers in the world during his time.
- The Nizam initially served as a viceroy or subahdar of the Mughal Empire and was responsible for governing the Carnatic subah.
- However, with the decline of the Mughal Empire, the Nizams of Hyderabad gradually gained more autonomy and became independent rulers in their own right.

Reasons for the authority of the Nizam of Hyderabad over the Carnatic subah:
1. Historical Role: The Nizams of Hyderabad had a long-standing association with the Carnatic region. They had played a crucial role in the Deccan politics and had established their authority over the region over time.
2. Mughal Appointment: The Mughal Empire had appointed the Nizam of Hyderabad as the subahdar of the Carnatic subah, giving him the administrative and political control over the region.
3. Military Strength: The Nizams of Hyderabad had a formidable military force, which further solidified their authority over the Carnatic subah.
4. Local Support: The Nizams also enjoyed the support of the local elites and nobles in the Carnatic region, which helped in maintaining their authority and control.

Overall, the Nizam of Hyderabad was the rightful authority over the Carnatic subah during the Mughal period. Their appointment by the Mughal Empire and their subsequent consolidation of power in the region gave them the necessary legitimacy and control over the administrative affairs of the Carnatic.