TASK DEFINITION: You will be given a trivia clue, and the category it belongs to. You should answer with the best answer that belongs in the category and is described by the clue. For simplicity, answers should be in all lower cased letters.
PROBLEM: Category: PATRIOTIC SONG TITLES 
Clue: "What so proudly we hailed at the twilight's last gleaming"

SOLUTION: the "star-spangled banner"

PROBLEM: Category: PARTICLE PHYSICS 
Clue: To get an element's mass number, add its protons & these

SOLUTION: neutrons

PROBLEM: Category: THE MONROE DOCTRINE 
Clue: The doctrine might have been issued jointly with Britain but for opposition from John Quincy Adams in this post

SOLUTION:
secretary of state