Concept:The correct phrasal verb is needed to describe an alarm that suddenly starts sounding.
Explanation:In English, we say that an alarm "goes off" when it begins to ring or sound unexpectedly.
Since the sentence is in the past tense, the correct form is "went off".
"Died off" means something gradually disappeared or stopped existing, which does not describe an alarm.
"Rang up" usually means made a telephone call, so it is not appropriate here.
"Ran off" means escaped or left quickly, which has no connection to an alarm sounding.
Therefore, the only option that correctly completes the sentence is "went off".
Answer:A. went off