First tell your rank in JEE mains because ranks are out and your percentile is good but main obstacle in admission is your board percentage because every institute has its own criteria for admission like all institutes have criteria of about 70% . So in my opinion you should have to reappear for improvement exam in board if you have another chance because admission in any good government institute is very hard with such low board percentage.

And most of private colleges also have criteria for percentage . According to me and as a mentor , you should reappear for improvement exam in board because board percentage matters a lot after completion of graduation. So think upon it.

I think this information help you out.