Hello,

Yes you can absolutely give jee mains exam because the eligibility criteria to attempt jee exams is the aspirant is appearing in class 12th or passed class 12 and you are appearing class 12 so you can give that exam and if you really want to give jee exam then you should give it .

As you says that your board exam is on next month there is no problem but youhave to manage your time for your board exam as well as jee exam..

You have to make daily routine, daily scheduled the topics you have to study,and just read for your board in very well manner and practice mcqs questions from good and popular books like arihant boks and do the time boundation practice you can do well ...

Hope it will help you

Thanks!!