is private degree eligible to sign for officer?
Three things:-
1. A Levels or Diploma already good enough for OCS.
2. OCS entry is based on BMT results, even for regulars. It's unlikely the SAF will fast-track you -- unless you've earned it on merit & THEN signing on, for example. Plus those Tekong instructors can sabo your career prematurely if you're clearly unqualified.
3. No such thing as "private degree". Anyone is free to study via distance-learning (i.e. private schools) or online courses, but better make sure their degrees are properly accredited by their source country & are also "recognized" in S'pore. Otherwise, even civilian employers won't necessarily hire you, if they're clueless about the quality of your academic/training course.