Option 1 -> The Ilbari dynasty is indeed famously called the Slave Dynasty (or Mamluk Dynasty) as its rulers were of slave origin who rose to power.
Option 2 -> The Khilji Dynasty was a separate dynasty that succeeded the Slave Dynasty in the Delhi Sultanate (1290-1320).
Option 3 -> The Tughlaq Dynasty was another distinct dynasty of the Delhi Sultanate that ruled after the Khiljis (1320-1414).
Option 4 -> The Lodhi Dynasty was the last dynasty of the Delhi Sultanate (1451-1526), not related to the Ilbari dynasty.
Hence, Option 1: The Slave Dynasty -> The Ilbari dynasty (1206-1290) was the first dynasty of the Delhi Sultanate, founded by Qutb-ud-din Aibak. It's called the "Slave Dynasty" because many of its prominent rulers, including Qutb-ud-din Aibak and Iltutmish, were originally slaves (mamluks) who rose through military service to become sultans -> correct