Eligibility for NEET and IIT high school and 12 th

From 1 year gap what I presume is after your class 10 you did not do anything for 1 full year and then joined class 11 and next year after qualifying class 11 you joined class 12.

If it is so the one year gap is not a problem but in the eligibity criterion for NEET it is very clearly mentioned that the student should have done 10+2 or equivalen with Physics, Chemistry, Biology/Biotechnology and English as core subject in both Classes 11 and 12 from a recognized board of education.

In view of the above please check whether you were having these subjects in class 11 as well as 12 as you will have to produce the credentials for them.

The qualifying marks for the unreserved category for appearing in NEET are 50% considering only Physics, Chemistry and Biology.

For IIT also the one year gap will not be a problem but the aggregate marks in your class 12 should be 75% or more and then only you can appear in the JEE advanced entrance exam.

After 10th class to complete 12th class you require minimum two years. There is a gap of one year. That means you passed 12th class after 3 years of your 10th class passing. Am I correct?
In such case, you will not have any problem to attend NEET exam. The education qualification for NEET is as given below.
Candidates must have passed the higher/senior secondary examination or ISCE which is equivalent to 10+2 examination Higher/Senior Secondary Examination after a period of 12 years study.
Candidates must pass the above qualifying examination with Physics, Chemistry, Biology/Biotechnology and English subjects.
Candidates must secure minimum 50% marks (GEN), 40% marks (SC/ST/OBC), 45% marks (GEN PH) & 40% marks (SC-PH/ST-PH/OBC-PH) taken together in PCB subjects.
Candidates who are in the 12th standard can also apply. They must have to show the passing certificates complying with the percentage criteria at the time of first round of counselling.
If you are fulfilling the above then one year gap is not a problem.
For IITs, one year gap is not an issue provided you fulfil all other criteria.

The upper age limit for appearing in NEET is 25 years for General Category candidates and 30 years for reserved category candidates. There is no stipulation regarding a one-year gap in XIIth standard. So, even if you lose a year in XIth standard or in XIIth standard, you will be able to appear in NEET provided you don't cross the upper-age limit.