Explanation:

- Nasir-ud-Din Mahmud was a ruler from the Mamluk Dynasty, commonly referred to as the Slave Dynasty.

- The Mamluk Dynasty was the first of the dynasties of the Delhi Sultanate, ruling from 1206 to 1290.

- Sayyid Dynasty emerged after the Tughlaq Dynasty and ruled from 1414 to 1451.

- Tughlaq Dynasty was the third dynasty of the Delhi Sultanate, ruling from 1320 to 1413.

- Lodi Dynasty was the last dynasty of the Delhi Sultanate, ruling from 1451 to 1526.

- Nasir-ud-Din Mahmud ruled in the mid-13th century, during the Mamluk Dynasty's reign.

The correct answer is Option: 4 - Mamluk.

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