Sultan Qutb-ud-din Aibak`s death is an historical event.

Options 1 suggests that Aibak was assassinated by a noble. However, there is no historical record indicating that Aibak was killed in such a manner.

Option 2 states that Aibak was killed in a battle with Taj-u-din Yildiz, the ruler of Ghazni, competing over Punjab. Although it`s true that there were conflicts between different monarchs for territorial control, but we don`t have any proof suggesting that Aibak died during one of these battles.

Option 3 suggests that Aibak was injured while besieging the fortress of Kalinjar in Bundelkhand and subsequently died from his injuries, but again the historical records do not support this claim.

Option 4, the correct answer, says that Aibak died from a fall from his horse while playing a game called Chaugan, a form of polo. This is the well accepted and historically documented cause of Aibak`s death. Hence Option 4 is the correct answer.