Correct Option (A):
Dewan-i-Bandagani was a department established by Firoz Shah Tughlaq. Its primary function was the administration, welfare, and employment of slaves (bandagans). Firoz Shah Tughlaq maintained a large number of slaves, integrating them into various state services and administration.
Incorrect Options:
Dewan-i-Mustakhraj was a department established by Alauddin Khilji, not Balban. Its purpose was to investigate and recover revenue arrears from corrupt officials and defaulters.
Dewan-i-Kohi was an agricultural department created by Muhammad Bin Tughlaq, not Alauddin Khilji. Its objective was to bring uncultivated land under cultivation and improve agricultural output through state support and direct grants to farmers.
Dewan-i-Arz was the military department responsible for the organization, recruitment, and administration of the army. It was established by Ghiyas ud din Balban, not Muhammad Bin Tughlaq, as part of his efforts to strengthen the central army.