The correct chronological order of building the given monuments is option-2: 3, 1, 2, 4.

Let`s analyze each option to understand why option-2 is correct:

Option-1: 3, 1, 4, 2 - This option suggests that the Qutub Minar was built first, followed by Tughlaqabad Fort, then Fatehpur Sikri, and finally the Bada Gumbad in Lodhi Garden. However, this is incorrect.

Option-3: 1, 3, 2, 4 - This option suggests that Tughlaqabad Fort was built first, followed by Qutub Minar, then the Bada Gumbad, and finally Fatehpur Sikri. Again, this is incorrect.

Option-4: 1, 3, 4, 2 - This option suggests that Tughlaqabad Fort was built first, followed by Qutub Minar, then Fatehpur Sikri, and finally the Bada Gumbad. However, this is also incorrect.

Therefore, option-2 remains as the correct answer as it correctly states the chronological order of the monuments: Qutub Minar