Explanation:

- Magadha: Magadha was a prominent monarchical state located in what is now the modern-day state of Bihar. It played a crucial role in the development of Indian history and culture.

- Avanti: Avanti was another significant kingdom situated in the present-day region of Madhya Pradesh. It was known for its capital cities, Ujjain and Mahishmati.

- Vaishali: Vaishali was not a monarchical state but rather a republic, known for its early democratic practices. It was part of the Vajji confederacy and located in modern-day Bihar.

- Kosala: Kosala was a major kingdom during this period, with its capital at Ayodhya. It was an influential and powerful state in ancient Indian history.

Based on the explanation, Vaishali was not a monarchical state.