Hi aspirant

There is no chance for PSUs/IITs/NITs .Yes you can apply in government/Private colleges which comes under your state.

With 35 marks only this is possible.And being a general category most probably there is less chance ofr that even too.But still if there are good numbers of seats in state colleges then you can easily get.

To precisely know which college/Psu you will get with your marks you can visit the GATE pathfinder by visiting the link given below:

https://engineering.careers360.com/gate-college-predictor

Hope this was helpful.