The correct answer is: A. Alauddin Khalji.
Alauddin Khalji was the second ruler of the Khalji dynasty of the Delhi Sultanate. He was a powerful and successful ruler who expanded the Delhi Sultanate to its maximum geographical limits. He conquered new territories in the Deccan Plateau, Gujarat, and Bengal. He also built a strong military and a well-organized administration.
Qutbuddin Mubarak Shah Khalji was the third ruler of the Khalji dynasty of the Delhi Sultanate. He was a weak and incompetent ruler who was unable to maintain the power and stability of the Delhi Sultanate. He was overthrown by his nephew, Muhammad bin Tughlaq.
Muhammad bin Tughlaq was the fourth ruler of the Tughlaq dynasty of the Delhi Sultanate. He was a brilliant but erratic ruler who expanded the Delhi Sultanate to its greatest extent. However, his ambitious policies and military campaigns led to the decline of the Delhi Sultanate.
Firuz Tughlaq was the fifth ruler of the Tughlaq dynasty of the Delhi Sultanate. He was a just and benevolent ruler who restored the stability and prosperity of the Delhi Sultanate. He built many mosques, madrasas, and hospitals. He also promoted agriculture and trade.
In conclusion, the Delhi Sultanate reached its maximum geographical limits during the reign of Alauddin Khalji. He was a powerful and successful ruler who expanded the Delhi Sultanate to its greatest extent.