Option 1 suggests that Alauddin Khalji first established a separate department for `ariz,` which is incorrect. Although Alauddin Khalji did enact military reforms, the establishment of the ariz`s department was done by Balban.

Option 2 implies that Balban was the person who introduced the branding system for military horses, but this claim is not accurate. It was Alauddin Khilji who instituted this system as a part of his military reforms to keep track of horses and deter theft and substitution.

Option 3 states that Muhammad bin Tughlaq was succeeded by his uncle to the Delhi throne, but this is also false. After Muhammad bin Tughlaq`s death, the throne was succeeded by his cousin, Firuz Shah Tughlaq.

Option 4, which is the correct answer, states that Firuz Tughlaq set up a separate department for slaves. This is true, Firuz Tughlaq established the Diwan-i-Bandagan or department of slaves. The department was responsible for the welfare, payment, and assignments of the slaves that were a part of Firuz Tughlaq`s administration.