B.Tech Computer Science and Engineering

I would suggest the integrated 5 year degree in VIT because firstly it will save you the trouble of again preparing for GATE exam for doing an B.Tech degree in case you feel interested in your field of study.
Secondly, by doing the integrated degree, you are saving one year time which could utilized more productively.
Thirdly, in case you feel of doing a Masters after finishing your Bachelors, you might get the glamorous idea of doing an MS from abroad which is usually not sponsored unless you join an integrated MS plus Ph.D program. Basically getting a scholarship for an MS degree abroad is really difficult and is pretty expensive (high dollar value against rupees). You can always look for a student loan to pay for the MS degree but why take all this pain when you can get the Masters degree easily by paying relatively cheaper tuition fee in India.

I think you should go and visit ICFAI University. Don't go just by the name. There are too many good colleges in Rajasthan, especially in Jaipur which are trying to compete with VIT Vellore, MNIT and LMNIT in terms of modern educational concepts, association with renowned universities in UK, USA, Canada and Russia sending their students in these institutions to compete globally, providing multidisciplinary expertise, opportunities for START-UPS their innovative ideas. In addition, they are providing project based learning from 1st semester and flexible-slot based time-table. I think you must visit some of the college in Jaipur specially Anand International College of engineering before making any decision. Please share your experience. All the best.