Birnathan, the Hindu kotwal, was associated with the reign of Firuz Tughlaq, who was the Sultan of Delhi from 1351 to 1388.

Firuz Tughlaq and his policies:
- Firuz Tughlaq was known for his administrative and economic reforms, which included the introduction of a new currency, irrigation projects, and establishment of hospitals and dispensaries.
- He also abolished many unpopular taxes and introduced new ones to increase revenue.
- Firuz Tughlaq was a patron of art and literature, and his court was known for its cultural activities.

Birnathan:
- Birnathan was a Hindu kotwal under Firuz Tughlaq's reign, which means he was the chief of police or law enforcement in Delhi.
- His appointment as kotwal was significant as it showed Firuz Tughlaq's policy of religious tolerance and inclusiveness towards Hindus.
- Birnathan was known for his efficiency and honesty in his duties as kotwal.

Other rulers and their policies:
- Balban was a Sultan of Delhi from 1266 to 1287, and he was known for his authoritarian rule and suppression of nobles and rebels. It is unlikely that he would have appointed a Hindu kotwal.
- Ala-ud-din Khalji was a Sultan of Delhi from 1296 to 1316, and he was known for his military conquests and administrative reforms. However, he was also known for his persecution of Hindus, and it is unlikely that he would have appointed a Hindu kotwal.
- Muhammad-bin-Tughlaq was a Sultan of Delhi from 1325 to 1351, and he was known for his eccentric policies, such as the transfer of his capital from Delhi to Daulatabad. However, there is no record of him having a Hindu kotwal.

Therefore, the correct answer is option D, Firuz Tughlaq.