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What kind of engineering have you been completed? Is it B.E/B.Tech or Engineering Diploma? The exam about you asked is for undergraduate programs like BMS and B.A. (Hons) and BBA-FIA conducted by Delhi University for its affiliated colleges also known as DU JAT (Delhi University Joint Admission Test) for shortlisting of candidates for above programs. The eligibility criteria for above programs is 10+2, Candidates should complete their higher secondary education in any stream (Science, Humanities, and Commerce) from a recognised board and obtain a minimum score of 60 percent in four papers including English, Mathematics and other two subjects from the list of elective subjects as approved by the University of Delhi.

As per UGC NET 2019 Eligibility you are not eligible on the basis of B. M. degree only. The detailed eligibility criteria is as under.
1. Age:- He/ she must not be more than 28 years as on January 1, 2019 for applying for Junior Research Fellowship. A relaxation of up to 5 years is provided for candidates belonging to reserved categories.
2. Academic Qualification :- For candidates who wish to appear for NET 2019 conducted by UGC, they must clear all the defined standards. Given below is the eligibility criteria to appear for NTA UGC NET 2019:
Candidate must have scored at least 55% aggregate marks (50% for SC/ST, OBC- NCL, PwD) in Masters Degree or equivalent examination from university recognised by UGC in Humanities (including languages) and Social Science, Computer Science and Applications, Electronic Science etc. To be eligible for UGC NET 2019. Candidates who are presently in the final year of their Masters programme or those who are waiting for their final year results can appear for UGC NET 2019 test.