IIT

Yes, you can give improvement exam for any subject of 12th class for meeting the JEE Main eligibility criteria of 75% aggregate marks. The CBSE improvement exams form will be available in the month of October every year.

As per the admissions 2020 The Eligibility for B.Tech is 60% in 10+2 with (English, Physics & Mathematics ) will have to appear in LPU NEST whereas those who have scored 90% in +2 or scored 90 percentile in JEE Mains are exempted from LPU NEST and moreover LPU has been ranked top 80 amongst all priv

No actually you are not eligible for admission in any government college, NIT, IIT or any other reputed private college like VIT, SRM, BITS PILLANI etc. This is because the eligibility for these are minimum 75% in class 12th. But definitely you can apply for any other private college those who don't