The correct answer is option 'A' - 1206-1210 A.D.

Qutb-ud-din Aibak was the founder and first ruler of the Delhi Sultanate in India. He was a slave of Muhammad Ghori, the ruler of Afghanistan, and was appointed as the governor of Delhi in 1192 AD after the defeat of Prithviraj Chauhan in the Second Battle of Tarain. Qutb-ud-din Aibak's period of rule can be divided into two parts - his reign as a governor and his reign as a sultan.

Reign as a Governor:
After being appointed as the governor of Delhi, Qutb-ud-din Aibak ruled from 1192 AD until 1206 AD. During this period, he consolidated his power and established his authority over the region. He established the Mamluk dynasty, which marked the beginning of the Delhi Sultanate. Aibak initiated the construction of the Qutub Minar, which later became a symbol of the Sultanate's power and influence. He also introduced various administrative reforms and policies to strengthen his rule.

Reign as a Sultan:
In 1206 AD, Qutb-ud-din Aibak declared himself the Sultan of Delhi, thus becoming the first Sultan of the Delhi Sultanate. His reign as a sultan lasted until his death in 1210 AD. As a sultan, he further expanded his territory and established his authority over the neighboring regions. Aibak was known for his military campaigns and successfully defended his kingdom against various invasions.

Although Aibak's reign was relatively short, he laid the foundation for the Delhi Sultanate and established a strong political and administrative system. He was succeeded by his slave, Iltutmish, who further consolidated and expanded the Sultanate.

In conclusion, Qutb-ud-din Aibak's period of rule was from 1206-1210 AD. He ruled as a governor from 1192-1206 AD and as a sultan from 1206-1210 AD. His reign marked the beginning of the Delhi Sultanate and laid the foundation for the subsequent rulers of the Sultanate.