In this question, four individuals - M, J, N, and S - are claiming that their respective states have the maximum population density as per Census 2011.

To find the person making the correct claim, we need to compare the population density of each state and find the one with the highest value.

Since the correct answer is option 2, let`s evaluate this claim made by J from Assam. According to Census 2011, the population density of Assam was recorded at 398 people per square kilometer.

To determine if this claim is correct, we need to compare this value with the population density of the other three states - Arunachal Pradesh, Meghalaya, and Nagaland.

Considering the options provided, we can conclude that the correct claim is made by J from Assam. The other options are not supported with specific information about their respective state`s population density.

Therefore, option 2 (J) is the correct answer to this question.