Yes, you can write the exam but if you get a good rank this time then you need to skip your present college. Also i guess if you are already pursuing a course in a college you should continue it but if you are not satisfied with it then it call. You can write the paper but your one year in this college will get wasted its not like that after this you will be transfered to 2nd year.
I would suggest think properly and then go for it what you think is good for you. All the best.
You totally can give it a second try. But if you're already doing your first year, I would personally suggest not to let this one year get wasted. However, improvement is always a good call. Also, if you want betterment, try reappearing for JEE once again as well.
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