Can I get admission in any IIITs or NITs by JEE Mains AIR 35038?

One of my close friends chose to go for Nirma Institute because of a rank like that, whether you'd want to believe it or not, but your rank and marks are not satisfactory.

If you'd wanted to get into the CSE program, then I must motivate you to strive better by saying that for CSE you need better scores. No IIT or NIT will grant you admission in the stream with 35038 ranks.

Although, you may still have a chance at NIT Srinagar for Chemical, Civil; NIT Silchar for Instrumentation Engineering; NIT Rourkela for Ceramics; and NIT Agartala for Chemical, Civil, Production engineering. These colleges have a good national reputation.

I'd suggest that you keep other options open like keep checking official websites of universities like Sharda University, Lovely Professional University, Nirma Institute etc.

You might get better opportunities here because they are much more advanced with state-of-the-art facilities. They do not have the reputation of an IIT but they have live projects, spectacular infrastructure, multidisciplinary programs and offer good exposure to students through association with academic delegates from India and abroad.