The correct statement(s) are mentioned in option 3, which says "Both 1 and 2".

To understand this, let`s analyze each statement:

1. Nilamoni Phukan Jr. is the 56th Jnanpith Award winner.

This statement implies that Nilamoni Phukan Jr. has won the 56th Jnanpith Award. If we consider this statement to be true, it means that Nilamoni Phukan Jr. is indeed the 56th Jnanpith Award winner.

2. Damodar Mauzo is the 57th Jnanpith Award winner.

This statement suggests that Damodar Mauzo has won the 57th Jnanpith Award. In this case, if we assume the statement to be true, it means that Damodar Mauzo is indeed the 57th Jnanpith Award winner.

Since both statements are true, option 3, which states "Both 1 and 2," is the correct answer.