Hello,
You can apply for Josaa counseling even if you have not qualified the JEE Advanced cutoffs and  you wish to take admission based on your rank obtained in JEE Mains. On the basis of JEE Mains rank and cutoffs of various colleges, you can get a seat. So, you can apply for Josaa counseling if you want to take admission in NITs, IIITs on the basis of your JEE Mains performance.
I hope it helps.

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