Hello Aspirant,

Eligibility criteria for IES or ESE are

Candidate must have received a degree in Engineering from a university integrated by an act of the central or state legislature in India or other educational institutions established by an act of Parliament or acknowledged as deemed to be universities under section-3 of the university grants commission act.

As NMIMS Mumbai is a private deemed university, you are eligible for this exam.

It came to be a deemed university organized under Section 3 of the UGC Act, 1956.

I hope it helps.