Hi Aspirant,

Yes, you can appear for JEE Exam 2021 even after appearing for class 12 improvement exam. In this case you will be considered as a student appearing class 12th rather than already passed student. However you have to see that you have given your 12th exam in 2021 for which you are writing the improvement exam because the eligibility criteria for JEE main clearly states that candidates should have passed class 12 or qualifying the exam in 2019 or 2020 or are appearing in class 12 or equivalent qualifying exam in 2021.

For further information you can refer the link below,

https://engineering.careers360.com/exams/jee-main

Hope this helps.

All the best!!!