Hi Ankur, 

As per the JEE Mains rules for improvement 2019, the points of concern are:

If a candidate passes Class 12 but writes one or a few subjects for improvement or any other reason, then top 20 percentile cut-off will be considered.

However, if a candidate writes all the subjects then the best of the two performances will be considered.

In case a Board does not provide information about the cut-off for the top 20 percentile, the candidate will have to produce a certificate from the respective Board stating that he/she falls within the top 20 percentile of successful candidates. If the candidate fails to do so, then the cut-off marks for the CBSE will be used.

If a candidate has passed Class 12th/ Equivalent qualifying examination from one state but appeared for improvement from another state, their state code of eligibility will be from where they have originally passed Class 12th/ Equivalent qualifying examination and not the state from where they have appeared for improvement.

Summarising: You are eligible to appear in JEE Main if you are appearing in improvement. Also, your marks in improvement exams will be valid for admission in IITs/NITs/IIITs and other CFTIs. You have to produce the mark sheet for the improvement exam at the time of counselling/admission.