Engineering Entrance Exam

Hello Yawar,
You may refer to the links below for the list of colleges that accept GATE exam scores:
1) https://www.shiksha.com/articles/institutes-accepting-gate-scores-for-me-mtech-phd-admissions-south-india-blogId-6655
2) https://www.shiksha.com/b-tech/articles/colleges-accepting-gate-scores-for-me-mtech-phd-admissions-north-india-blogId-6654

Hello,
There are many exams to get into IIT & NITs for the different courses and at the different levels:
IIT JEE: IIT JEE is the very first exam taken after the completion of class 12th for the Bachelor's degree at IITs and NITs.
IIT JAM : IIT JAM exam is also a national level entrance exam conducted for the UG students to pursue their Master's degree in science (M.Sc) at IITs & NITs.
GATE: GATE is another national level entrance exam conducted for the UG students to pursue M.Tech. at the IITs & NITs.
CAT: CAT is an exam conducted for the management student to pursue a management course from the IITs.

Do not waste your time, it is the most important thing. Pick up a NCERT and finish up. Go for the books which you need and finish it. After finishing up the books, solve sample papers. Mathematics will have to be practised daily.
All the best.

You can get in many private engineering colleges which have their own set of criteria for admission. I would suggest you for UEM Kolkata and to know more about the college visit here:
https://www.shiksha.com/university/university-of-engineering-and-management-kolkata-47398

First study NCRT books, they are suitable for this preparation.

Yes, you can but you need to clear your backlogs before the completion of 4th year of your BE degree.

I have heard that BASE Education is definitely the best JEE coaching around. They provide all kinds of study materials. They have many centers in Karnataka. If you want to seriously crack the JEE, BASE is the coaching you can opt for.
http://www.base-edu.in/