Ghiyas ud-din Balban had set up a _________ department called 'Diwan-i-arz'.

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- Historical context: Ghiyas ud-din Balban (reigned $1266	ext{--}1287$) was a ruler of the Slave (Mamluk) dynasty who reorganized the state machinery.

- Role of Diwan-i-Arz: The term "Diwan-i-arz" refers to the military department. Its duties included maintaining the army rolls, recruitment, deployment, discipline and payment of soldiers.

- Conclusion: Since Diwan-i-arz managed military affairs, the correct choice is option $1$ (military), corresponding to answer **a**.

FINAL_ANSWER: a

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