Hi, candidate you can not apply for private IIT mumbai. As IIT mumbai eligibility criteria includes JEE scores.

Thanks.

Hello,

IIT Mumbai accepts only admissions through JEE advanced score for studying undergraduate courses and GATE for Mtech courses, CEED (Common Entrance Exam for Design) for M. Des and PhD programmes, UCEED (Undergraduate Common Entrance Exam in Design) for B.Des programs, JAM (Joint Admission Test for M.Sc.)

Hope this helps....