Hey Ramalakshmi, 

Unfortunately no college I'm Andhra Pradesh provides a free seat for engineering. But there are some government colleges whose fees is almost negligible. If those are the colleges you are talking about. 6880 is a good rank. If you belong to general category,  then there are almost no chances to get into a good branch in AU and JNTUK. But if you can compromise for branches like chemical,  environmental,  petroleum etc. then you might get a seat in AU and JNTUK. But you can definitely target other JNTUs. There are very good chances that you might get a seat in JNTU Vijayanagaram.