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No!
Simple. I've achieved a rank under 10k but still prefered NIT over the IIT's available at this rank.
Infact you can safely assume that around 15k students 20k would opt for NIT over IIT.
The simple reason is qualifying JEE advanced should not be the motive but cracking the IIT under 5k should be the motive.
All the best
Hello Rangnath!
The cut off for JEE advanced 2019 for getting into IITs carries opening and closing rank for College and branch. The cut off is declared for each IIT and each branch separately.
For each IIT cut off will be declared online, and irrespective of being in the range of opening and closing rank you will have to meet the oficial cut off for the required stream/ branch.
I request you to go through this link for more clarity; https://engineering.careers360.com/articles/jee-advanced-cutoff-for-iits
All the best!
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