Explanation:
The target database must be mounted or open. Incorrect Answer:
1: You can do RMAN backup with mounted database als
2: It is not required that database must be closed: if it runs in ARCHIVE LOG mode you can perform a RMAN backup on mounted or open database.
3: You can do RMAN backup with opened database also.
Reference:
OCP Oracle 9i Database: Fundamentals II Exam Guide, Rama Velpuri, p. 269-270
Chapter 11: RMAN Backups

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