The correct answer is option 3: Muhammad-bin-Bhaktiyar. Muhammad-bin-Bhaktiyar was a Muslim adventurer who destroyed the Nalanda University. Nalanda University was a renowned Buddhist center of learning located in present-day Bihar, India. It was a center of excellence for education and attracted scholars from all over the world.

Option 1, Alla-ud-din Khilji, was a ruler of the Khilji dynasty in medieval India, but there is no historical evidence to suggest that he was responsible for the destruction of Nalanda University.

Option 2, Muhammad-bin-Tughlak, was a 14th-century ruler of the Tughlaq dynasty, but his reign was marked by administrative and financial reforms rather than acts of destruction.

Option 4, Muhammad-bin-Qasim, was an Arab general who invaded the Indian subcontinent in the 8th century, but he did not have any direct association with Nalanda University.

Therefore, the correct answer is option 3: Muhammad-bin-Bhaktiyar.