The construction of Qutub Minar was completed by

Iltutmish

In 1200 AD, the founder of the Delhi Sultanate, Qutb al-Din Aibak, began construction of  Qutb al-Dinar. In 1220, Aibak's successor and his son-in-law, Il Tumish, added three floors to the tower.

Hence, the correct option is (B) i.e, Illtutmish