Correct Option
Statement 2 is correct.
The Mysore Kingdom originated as a feudatory state under the Vijayanagara Empire. Following the decline and eventual disintegration of the Vijayanagara Empire, particularly after the Battle of Talikota in 1565, the Wodeyar dynasty of Mysore gradually asserted its independence. By the early 17th century, Mysore had established itself as an autonomous kingdom, evolving directly from its status as a vassal of the Vijayanagara Empire.
Incorrect Options
Statement 1 is incorrect.
The Nizamat of Arcot (Carnatic) was originally a subah (province) of the Mughal Empire. With the weakening of central Mughal authority in the early 18th century, the Nawabs of Arcot became virtually independent. It did not emerge from the Hyderabad State. Although the Nizam of Hyderabad later asserted suzerainty and influence over the Carnatic, and there were conflicts between the two powers, Arcot's origin was directly from the Mughal administrative structure, not as a splinter of Hyderabad.
Statement 3 is incorrect.
The Rohilkhand Kingdom was established by Afghan chieftains, known as Rohillas, in the Gangetic plains (present-day western Uttar Pradesh) during the period of Mughal decline. These Afghan settlers formed an autonomous state under their own leadership. It was not formed out of territories occupied by Ahmad Shah Durrani. While the Rohillas sometimes allied with Ahmad Shah Durrani, notably during the Third Battle of Panipat in 1761, their kingdom's formation and existence were independent of Durrani's territorial occupations.