I did my 12th in 2019 from CBSE board but unfortunately I got Compartment in math
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Hello
By private if you mean NIOS yes you can do that and there would be no problem since many students do study from NIOS and prepare for JEE Mains side by side there would be an option for NIOS in that section or something like that.
To know more check this link: https://learn.careers360.com/engineering/jee-main/.
Hope that helps.
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