Yes you need to pay fee even after clearing Jee to get into iits or nits. The mess charges are different for different colleges and the tution fee is around 120000 per semester in iits.

But if your family income is below 1 lakh you need not pay tution fee and you have to submit your income certificate. If it is between 1-5 lakh then you need to pay 1/3 rd of the tution fee and for this also you need to submit income certificate.

The fee structure in different iits is given in the following link.

https://engineering.careers360.com/articles/iist-btech-cutoff