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The eligibility criteria of Integrated M.Tech programmes of VIT Vellore is given below. Eligibility criteria : A pass in Higher Secondary Examination conducted by the State / Central Board of Secondary Education or its equivalent examination with 65% aggregate in Physics Chemistry and Mathematics (PCM). Admission criteria : The Admission will be on the basis of the performance in the qualifying examination (10+2). Candidates will be called for the counseling in the order of merit based on the aggregate of total marks secured in the +2 / Higher Secondary Examination, Your 10+2 marks are very good enough for getting admission here for Integrated M.Tech courses. So you will definitely get here.

I am not sure which university you are referring to. However, I can tell you that there are several universities in Vadodara that offer B.Tech courses and hostel facilities for students. For example, Parul University has hostel facilities for both girls and boys with an average fee of INR 1,18,000 per year. Maharaja Sayajirao University of Baroda also has hostel facilities for both girls and boys with an average fee of INR 9,800 per year. Indian Institute of Information Technology Vadodara has hostel facilities for both girls and boys with a fee of INR 30,000 per year. Drs. Kiran and Pallavi Patel Global University also provides hostel facilities for students.