Hello student, 

As you have mentioned that your gmr rank is 3863 which indeed is somewhat high. So, it is difficult to say that whether you can get government colleges or not... but it is certain that there will a great chance to get top private colleges according to previous year cut off and based on your rank...... But being in a positive side if you don't belong to general candidate you hold some decent chances to get a seat in the government colleges also....
So, don't loose hope and wish for the best!!!!
I hope this would help you.