There are no such procedures available for a passed out to student to again appear as a private student in the official website of the CBSE. So if you need to go through this procedure then I would recommend you to contact the CBSE officials directly will be more helpful. Now apart from this I would recommend that if you wish to get admission in engineering college, then NIOS will be a good option to study and to get the 10+2 certification from there with mathematics.

To know more about NIOS visit the link below:

https://school.careers360.com/exams/nios-class-12

I hope this answer helps. All the very best for your future endeavors!