Indian Institute of Technology, Delhi

The eligibility criteria of MBA from IIT-D (DMS) is given below. Eligibility criteria : A Bachelors Degree or equivalent with minimum 60% of aggregate marks or 6.00 CGPA on a 10 point scale. The Bachelors degree or equivalent qualification obtained by the candidate must entail a minimum of three years of education after completing higher secondary schooling (10+2) or equivalent. A relaxation of 5% in marks (I. e. min. 55%) or equivalent in CGPA (I. e. min. 5.50 on a 10-point scale) for the SC/ST candidates. Relaxation in criteria for PH candidates may be as per the Institute rules. Those having applied to IIT Delhi MBA programmes on qualifying the CAT will be shortlisted and then invited for a WAT and interview. Hence as per eligibility criteria you are eligible for MBA programme at IIT-DMS, Hence apply for CAT exam for further selection process.

IIT Delhi did not mention any particular one. But the Admission Policy for NIT students is :
Students who are enrolled under National Institute of Technology will have to score a CGPA (cumulative grade point average) of 8 by the end of their third year (6th Semester) of the B.Tech programme will be able to sit for an interview round, which will be the deciding factor for admission into the Ph.D. course. Shortlisted students will be capable to take admission in Ph.D. directly without appearing for GATE exam. This scheme is only applicable for the students who are enrolled under 4th year of B.Tech course at astonishing NITs premise across the country.

They did not mention specific names. But the Admission Policy for NIT students is :
Students who are enrolled under National Institute of Technology will have to score a CGPA (cumulative grade point average) of 8 by the end of their third year (6th Semester) of the B.Tech programme will be able to sit for an interview round, which will be the deciding factor for admission into the Ph.D. course. Shortlisted students will be capable to take admission in Ph.D. directly without appearing for GATE exam. This scheme is only applicable for the students who are enrolled under 4th year of B.Tech course at astonishing NITs premise across the country.