Well, I read the question again and changed my mind.

It implies that files are restored from the cold backup, so archive logs and online redo logs included in the backup are useless (if the database was cleanly checkpointed and shutdown, what is the correct for a cold backup).

The archive logs and online redo logs that should be applied after the database is restored probably will be in disk. These files were generated AFTER the cold backup (and are not included in that), so they weren't backed up yet.

So, there are the following possibilities:
a) Archivelogs and online redologs after backup available; database in ARCHIVELOG => Restore control files and datafiles and then recover (answer #3)

b) Archivelogs and online redologs after backup unavailable; database in NOARCHIVELOG => Restore control files and datafiles and then open the database without recovery (answer #3)


However, the correct answer is #4.

pretty strange question.