Consider the following dynasties: 1. Hoysala 2. Gahadavala 3. Kakatiya 4. Yadava How many of the above dynasties established their kingdoms in early eighth century AD?

Let's examine the period of establishment and prominence for each dynasty:

Hoysala: The Hoysala dynasty rose to prominence in the Karnataka region from the 10th century onwards, with their peak influence in the 12th-14th centuries. They did not establish their kingdom in the early 8th century AD. Gahadavala: The Gahadavalas ruled parts of Uttar Pradesh and Bihar, with their significant rise to power in the late 11th century and dominance in the 12th century (c. 1089-1194 CE). They were not present in the early 8th century AD. Kakatiya: The Kakatiya dynasty rose in the Andhra region, gaining prominence from the 12th century and ruling till the 14th century (c. 1083-1323 CE). They were not established in the early 8th century AD. Yadava: The Yadava dynasty of Devagiri (Maharashtra) emerged as a significant power in the late 12th and 13th centuries (c. 1187-1317 CE). They were not established in the early 8th century AD. All the listed dynasties established their independent and prominent kingdoms much later than the early 8th century AD. Therefore, none of the above dynasties established their kingdoms in the early eighth century AD.