Yes they're eligible because if you passed your 12th from CBSE then you are eligible for writing neet.

Hi Hitesh
Private student are eilgible to get admission in Ucms but you to have better score in neet examination .And expected cutoff for Ucms is above 600 if you are  general category student from outside Delhi because Ucms has 85%reserved Delhi domicile student . If you are Delhi domicile student the expected cutoff is 550 to 580 in neet examination . So do not get worried about such thing work hard perform well in examination .
All best you Carrer
Hope you understand Hitesh
Good luck

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