When did the first independent ruler Qutubud-din-Aibak establish the Slave…

Concept: A dynasty's founding year is the year its first ruler formally broke away from the preceding power and assumed independent sovereign authority -- not the year a predecessor died of unrelated causes, a later ruler within the same line acceded, or the dynasty eventually ended.

Application: Sultan Muhammad Ghori of the Ghurid Empire was assassinated in 1206 AD. His trusted Turkic slave-general (mamluk), Qutb-ud-din Aibak, who had been governing Ghori's Indian territories from Delhi, used this moment to have himself formally enthroned as an independent Sultan at Lahore in 1206 AD, cutting ties with the Ghurid empire. This act of independent enthronement in 1206 AD is what marks the founding of the Slave (Mamluk) dynasty -- the first of the five dynasties that together made up the Delhi Sultanate.

Cross-check -- why the other years do not fit:

• 1260 AD falls in the middle of Sultan Nasir-ud-din Mahmud's reign (1246-1266 AD), decades after the dynasty had already been founded.

• 1266 AD is the year Ghiyas-ud-din Balban ascended the throne -- a later succession within the already-established dynasty, not its founding.

• 1276 AD falls within Balban's own reign (1266-1287 AD), again long after the dynasty's founding.

Only 1206 AD is the year Aibak established independent rule, so 1206 AD is the founding year of the Slave dynasty.