While answering I'm just writing what I think, but it's only and only you who have to decide what you want to do in your career. 3rd attempt may seem too big and challenging for jee mains but, then again it is totally upto you what you want, If you want a good college, good placement a tag of NIT'IAN or something like that and if you have that zeal then go on no one can stop you chasing your dreams, and it'll be definitely good for you.
But If you are in doubt or you are not clear with what you doing just quit it, don't chase anything only because it is dream of your parent something like that, discover your goals and chase them.

As far as placements are concerned, major companies have recruiting policies which stats that you may have only one year gap between your school and graduation, and if it's more you have to mention why it was and explain to recruiter with strong reason and with 3rd drop it might get bit more difficult for you.

So choose wisely it is your career and your life.
Thank you and best wishes.

I don't think so, you should go for any better college this year only ..I think 2nd drop might prove to be dangerous..

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