The correct answer is option 'B', Arunachal Pradesh.

Explanation:
Arunachal Pradesh shares the longest border with Myanmar among the given Indian states. Here are the details explaining this:

1. Location of Arunachal Pradesh:
Arunachal Pradesh is located in the northeastern part of India. It is bordered by several states of India as well as international borders with Bhutan, China, and Myanmar.

2. Geographical Location:
Arunachal Pradesh is situated in the easternmost part of India and shares its eastern boundary with Myanmar. The border between Arunachal Pradesh and Myanmar is formed by the Patkai Hills and the Naga Hills.

3. Length of the Border:
The border between Arunachal Pradesh and Myanmar is approximately 520 kilometers long, making it the longest border that India shares with Myanmar.

4. Importance of the Border:
The border between Arunachal Pradesh and Myanmar is of strategic importance due to its proximity to China. The area is a sensitive region from a security standpoint, and the border is closely monitored by security forces to prevent any illegal activities or incursions.

5. Cultural and Economic Ties:
The border region has a significant population of people belonging to various tribes, such as the Tangsa, Naga, and Singpho. These tribes have cultural and historical links with Myanmar, which contribute to the socio-economic ties between the two regions.

Conclusion:
In conclusion, among the given Indian states, Arunachal Pradesh shares the longest border with Myanmar. This border is strategically important and has cultural and economic significance for both India and Myanmar.