Hello,
Yes you can take part in the JOSAA counseling and also the CSAB spot round. The cutoff marks are only there to determine whether you have qualified for JEE advance or not. So anyone can appear for the JOSAA counseling. But the point is that it is useless. Anyone with rank above 80k won't get any government colleges like NITs or IIITs. All the seats get exhausted till then. With your rank you have zero chances of getting a seat. So I would highly recommend you to go for some good private engineering colleges like Sharda, Amity, Manipal etc.

Here's a list of some of them
https://www.google.com/url?sa=t&source=web&rct=j&url=https://engineering.careers360.com/colleges/ranking/top-private-engineering-colleges-in-India%3Fpage%3D1&ved=2ahUKEwiV17yo0IniAhUQXisKHTFZCkMQFjAMegQIARAB&usg=AOvVaw16NeVmi-WQRohTZE-NHiWB

Mata Sito Devi College of Education, Mansa

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