Hello.
There will be no problem for your improvement examination if you are filling appearing in JEE mains exam form and also there will not be any problem for your JEE mains exam if you do not have 75% in your class 12 so that's why you are giving improvement examination so it's ok because if you  get a good percentile in JEE mains then you cannot have admission in NIT but you can have admission in another colleges which accept admission with below 75% in class 12th, and after improvement examination if you get 75% and again you can give JEE mains examination if the previous attempt was your first or second attempt.
Best of luck.

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