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My opinion is you can do B.Tech from a private college. The best B.Tech private college is The Northcap University. Computer Science is an area that is evolving each day with new innovations that have been changing the globe over the last 50 years. The Department of Computer Science and Engineering is one of the core departments of The NorthCap University. The Department is striving towards its goal of providing innovative and quality education with high standards to achieve academic excellence. Keeping in view the dynamic nature of growth in industry and the increasing demand for the latest technologies, the department is starting five new specializations in B.Tech CSE namely.
1) Data Science and AI
2) Cyber Security
3) IOT & Cloud Computing
4) Full Stack Development
5) Game Tech, AR and VR
Visit: https://www.ncuindia.edu/.

Hello Nikhil,
The possibility is high to get an IIT if you drop a year and study, but you need to really work hard and you must be passionate towards your goal. The time of one year is really huge and so it should be used wisely, otherwise, it is better to get admission in any engineering college with your board exam marks.
If you are determined to study and dedicated towards your studying then you can get, but according to me, only if you can really work hard then you drop a year. Otherwise, don't waste your time.
The continuity of study is really important so that it is better to go to an engineering college now itself, but if you can, then drop a year.
Your confidence is the one which determines your admission into an IIT.
I would advise you to join a good IIT coaching centre as they will guide you properly. It is your wish only to drop a year., but if your board exam score is good, you can take admission in a good engineering college also. As many who have dropped a year also failed to clear JEE Advanced.
All the best.