Correct Option (A):
The Nizam Shahi dynasty of Ahmadnagar came to an end in 1633 when the Mughal Emperor Shah Jahan annexed the kingdom into the Mughal Empire. The last ruler of the dynasty, Hussain Shah Nizam Shah III, was captured by the Mughal forces and subsequently imprisoned for life. This marked the definitive absorption of Ahmadnagar into the Mughal dominion.
Incorrect Options:
Option 2 is incorrect. While the Mughals did capture the fort of Daulatabad, the last Nizam Shahi ruler, Hussain Shah, was imprisoned rather than killed during the siege. The term "Nizam-ul-Mulk" was a title, and the specific ruler at the end was Hussain Shah.
Option 3 is incorrect. Fateh Khan, son of Malik Ambar, was a powerful noble who played a significant role in the internal politics of the Nizam Shahi kingdom, even briefly usurping power and placing puppet rulers. However, his actions were part of internal power struggles and did not constitute the final end of the dynasty, which was ultimately brought about by Mughal conquest.
Option 4 is incorrect. Malik Ambar, the influential regent and military leader of Ahmadnagar, died naturally in 1626, not in 1631. The dynasty continued for several years after his death. Furthermore, the entire royal family was not killed; the last ruler, Hussain Shah, was imprisoned.