Hello,
The decision is completely on you. If you believe you can give full one year dedicated preparation to JEE and have the calibre to crack it, than only you should go for it.
However college name barely matters these days. Most companies look for skilled candidates rather than the college tag. Going for a private college and working hard to develop relevant skills to your trade will offer a wide spectrum of opportunities in your career.
Other factors such as coaching fee should also be considered.
Hope it helps , good luck.

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