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Dewan-i-Bandagani was a department established by Ghiyas-ud-din Tughlaq, hence option 1 "Dewan-i-bandagani ... Tughlaq" is correctly matched. He formed this division to manage public works and welfare schemes.
Analyzing the other options:
Option 2, "Dewan-i-Mustakhraj ... Balban" is incorrect. There`s no historical record of a department named Dewan-i-Mustakhraj established by Sultan Balban.
Option 3, "Dewan-i-Kohi ... Alauddin Khilji" is also mismatched. Dewan-i-Kohi was created by Firoz Shah Tughlaq, not Alauddin Khilji. It was aimed at developing wasteland agriculture.
Option 4, "Dewan-i-Arz ... Muhammad Tughlaq" is also incorrect. Dewan-i-Arz was a military department, but it was established by Alauddin Khilji, not Muhammad Tughlaq.
In conclusion, only option 1 correctly matches the department with the ruler who established it.