Question

in which sufi saint's memory was the qutub minar built

Answer 1

It was built by qutub ud din aibak a slave of muhammad ghori but due to qutub's death it remained incomplete after then Itutmish compluted it's construction.
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Answer 2

Qutub minar was made in the memory of Qutubuddin-Bakhtiyar-Kaki by Qutubuddin Aibak and was completed by Qutubuddin Aibak's son-in-law ÎLTUTMISH.