Which Sultan shifted the capital of the Delhi Sultanate from Lahore to Delhi and completed the Qutb Minar?

The correct answer is B, Iltutmish. Shamsuddin Iltutmish, who ruled from 1211 to 1236, moved the seat of government from Lahore to Delhi, completed the Qutb Minar that his father-in-law had begun, issued the silver tanka and the copper jital, organised the iqta system of land assignments and formed the Turkan-i-Chihalgani, the corps of forty Turkish nobles. He is therefore called the real consolidator of the Sultanate. Option A is wrong because Qutbuddin Aibak founded the dynasty in 1206 and kept Lahore as his centre; he only began the Qutb Minar and died in 1210. Option C is wrong because Balban came much later, from 1266 to 1287, and is remembered for the sijda and paibos ceremonies and for breaking the power of the Forty. Option D is wrong because Jalaluddin Khalji founded a different dynasty in 1290, long after the capital had moved.