The correct answer is: C. 1337 AD.
Mohammad-bin-Tughlaq captured the Nagarkot fort in 1337 AD. He was the second Sultan of the Tughlaq dynasty of the Delhi Sultanate. He was a powerful and ambitious ruler who expanded the empire to its greatest extent. He was also a controversial figure who was known for his erratic behavior and his unpopular reforms.
The Nagarkot fort is located in the present-day Indian state of Jammu and Kashmir. It was built in the 11th century by the Chauhans of Ajmer. It was an important strategic fort that controlled the trade routes between India and Central Asia.
Mohammad-bin-Tughlaq captured the Nagarkot fort after a long siege. The fort was defended by a large garrison of Rajput soldiers. The Tughlaq army was able to capture the fort by using their superior numbers and firepower.
The capture of the Nagarkot fort was a major victory for Mohammad-bin-Tughlaq. It gave him control of a key strategic fort and it also boosted his morale and that of his army.
The capture of the Nagarkot fort also had a significant impact on the history of India. It marked the beginning of the decline of the Chauhans of Ajmer and it also paved the way for the expansion of the Tughlaq empire.
The other options are incorrect because they are not the years in which Mohammad-bin-Tughlaq captured the Nagarkot fort.