Congratulations for your results. 

With 6500 rank in advance you can get in old IIT'S but you have to compromise on branch.

With 4964 rank in mains you will get good nit with good branches.

And wuth 345 marks in BITSAT you will get any branch in bits goa and hyderabad and in pilani campus you will be eligible for mechanical, chemical and electronics and instrumentation engineering according to last year data. 

Hi

In such situation you will get seats easily in any of the country's prestigious institutions. 

Beginning with JEE Advanced marks, you can IITs but not the best branches. See what you can get as per 2018 JEE Advanced Closing ranks - 

IIT Kharagpur 

IIT Roorkee

IIT BHU Varanasi

IIT Guwahati

IIT Gandhinagar

IIT Jodhpur

IIT Patna

ISM Dhanbad.

As per your JEE Mains Score you can get easily the top NITs and IIITs as well as the best GFTIs.

And as per your BITSAT marks, you can get the following in BITS Pilani Campus - all branches except B.E. Computer Science. You might get B.E. Computer Science at BITS Hyderabad Campus and  Goa Campus.

Check this link to know about BITSAT Cutoff : https://engineering.careers360.com/articles/bitsat-cutoff.

Check this link to know about NIT Cutoff : https://engineering.careers360.com/articles/jee-main-cutoff.

Check this link to know about JEE Advanced Cutoff : https://engineering.careers360.com/articles/jee-advanced-cutoff.

Best of Luck.

Hope this helps.

Cheers!

If you belong to general category then I suggest you to go for nit . You scored very descent score in JEE mains . You can get admission in some top nits. I am sharing you the list of some college.

• Nit Warangal
• Nit surathkal
• Nit Bhopal
• Nit Calicut
• Nit Allahabadh
• Nit Surat
• Nit Jaipur

You will be able to get admission in IIT but you have low chances to get a descent branch.

All the best