Explanation:

The Nizamat of Arcot: This did not emerge from Hyderabad State. The Nizamat of Arcot was established in the Carnatic region under the Mughals, and it was distinct from Hyderabad. Hyderabad was under the Nizams, while Arcot was under the Nawabs of Carnatic.

The Mysore Kingdom: The statement is correct. After the decline of the Vijayanagara Empire, several smaller kingdoms, including the Mysore Kingdom, emerged in the region that was once controlled by Vijayanagara.

Rohilkhand Kingdom: The Rohillas were Afghan settlers who established their dominance in the Rohilkhand region of North India. However, they didn't form their kingdom out of territories occupied by Ahmad Shah Durrani (also known as Ahmad Shah Abdali). They were in India before the invasions of Ahmad Shah Durrani.

Thus, the only correct statement is the second one.