The correct answer is option 1, Manipur. Manipur is an Indian state located in the northeastern part of the country. It shares its borders with the states of Nagaland to the north, Mizoram to the south, and Assam to the west. However, Manipur does not have a common international border with Bangladesh.

Option 2, West Bengal, is incorrect as it does have a common international border with Bangladesh. West Bengal shares a significant stretch of its border with Bangladesh.

Option 3, Tripura, is also incorrect as it shares its entire eastern border with Bangladesh. Tripura is a small state located in the northeastern part of India.

Option 4, Assam, is also incorrect as it shares a portion of its border with Bangladesh. Though Assam is not entirely surrounded by Bangladesh, it has a common international border with the country.

In conclusion, the Indian state that does not have a common international border with Bangladesh is Manipur.