I'm sorry to inform you that there is no centrally funded engineering institute which take admission directly .In centrally funded institutes for admissions in engineering one can get only on the basis of JEE Score. 

In State funded Technical institute the admissions for engineering are done on the basis of marks scored in entrance exam conducted by that particular state. 

In most of private institutions admission in engineering is done on the basis of marks scored in the entrance exam conducted by that particular institution. Rarely any private institution takes admission through only academics. 

If you still have any queries feel free to ask in the comment section down below.