Hello Sanjeeb,

Yes ,if you have passed your 12 examination you can definitely give neet exam.It doesn't matter if you have passed from cbse ,nios or are a private candidate.

Just keep in mind that as information of 11 needs to be submitted while form filling,

They ask the name of school ,year of passing and school address ,just add the 12 details of private in name and address and for year of passing use one year before your 12 passing year.

Use the site for more details.

https://www.google.com/amp/s/medicine.careers360.com/articles/neet-2018-what-nios-students-and-private-candidates-should-know/amp

Good luck.