The ruler who famously refused to merge his state with India and was subject to a popular revolt was the Nawab of:

Junagadh
Palanpur
Radhanpur
Kutch

The correct answer is: The Nawab of Junagadh.

The Nawab of Junagadh, Muhammad Mahabat Khan III, famously refused to merge his state with India and was subject to a popular revolt. He instead acceded to Pakistan, which was a decision that was not supported by the majority of the population of Junagadh. This led to a popular revolt, which was eventually put down by the Indian army. The Nawab was eventually forced to abdicate and Junagadh was merged with India.

The other options are incorrect. The Nawab of Palanpur, Ibrahim Khan II, acceded to India without any problems. The Nawab of Radhanpur, Fateh Muhammad Khan, also acceded to India without any problems. The Nawab of Kutch, Mahabat Khan II, acceded to India after some initial hesitation.

The Nawab of Junagadh was the only ruler of a princely state in India who refused to merge with India. His decision to accede to Pakistan led to a popular revolt and eventually to the Indian army taking over Junagadh. The Nawab was eventually forced to abdicate and Junagadh was merged with India.