The correct answer is (b) 1500 BC to 500 AD.
The Katyuri dynasty was a Hindu dynasty that ruled over parts of present-day Uttarakhand in India from the 15th century BC to the 5th century AD. The dynasty was founded by Katyur, a descendant of the Pandavas, the heroes of the Mahabharata. The Katyuris were a powerful dynasty and their rule saw a period of great cultural and economic prosperity in the region. The dynasty came to an end in the 5th century AD, when it was overthrown by the Gupta Empire.
Option (a) is incorrect because it is too early. The Katyuri dynasty did not exist in 2500 BC.
Option (c) is incorrect because it is too late. The Katyuri dynasty ended in the 5th century AD, not the 15th century AD.
Option (d) is incorrect because it is not a period of time that the Katyuri dynasty ruled.