The correct option being "None" indicates that none of the listed dynasties—Hoysala, Gahadavala, Kakatiya, and Yadava—established their kingdoms in the early eighth century AD. The Hoysala dynasty emerged later in the 10th century, while the Gahadavala and Kakatiya dynasties also rose to prominence in the 11th century onwards. The Yadava dynasty began to consolidate power in the late 9th century but reached its zenith later. This understanding is essential for the UPSC Prelims, as it highlights the chronological context of medieval Indian history, emphasizing the need for precise timelines when studying dynastic rule and regional developments.