IIT

Excluding IITs and nits BITS PILANI has the highest placement record in India. Followed by LPU and Amity etc.

Yes, it's better to make your basics strong before proceeding further.

You will be asked during counseling about your extra co-curricular activity, then you can mention in them.

Yes, one year is sufficient for IIT preparation.

At this time, Resonance is best for IIT preparation.

In my opinion resonance is best for IIT preparation for freshers as well as repeaters. Best of luck.

Kotak is the best in term of IIT preparation. If you spending money then Kotak is the best option as it has a better atmosphere for study and competition.

For JEE Mains preparation, I suggest you Resonance.

Prepare on your own. Don't rely on any coaching institute, instead get a good internet connection and start studying online. This will be the best way to study and get the most out of your time. What you need is to focus your class 12th books Basics. NCERT textbooks are the best for IIT preparation. Just go through the books very thoroughly and then finally give lots of mock tests etc. To get a nice practice.

Click on the link for more details:-https://www.shiksha.com/b-tech/ranking/top-engineering-colleges-in-india-accepting-jee-mains/44-2-0-0-6244