Hello Aspirant
If you are not able to clear your 12th grade's compartment exam in one go, then CBSE gives you the freedom to appear either for that exam or other subjects as well as a private candidate. All you need to do is register yourself as a private candidate on the CBSE Board's official website. They ask you to fill out a form and give the details. This form is open only when there are 3-4 months left before the board exams commence.
There are no restrictions on a candidate to appear for CBSE exam as a private candidate even after clearing their papers because they may wish to appear for it for many reasons such as getting better marks, same as you.
For more accurate details and dates, please keep referring to the official website of CBSE website.
Hope this helps
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