Yes..you can..Everything is possible if one puts hardwork and determination for the goal.
Now coming to the practical process, since you have mentioned that your class 11th is weak,so i am assuming that didn't pay much attention to your studies in class 11th.Beforebgoing further into the preparation the first and foremost thing you need to do is to go back into the chapters of class 11th and study what you have missed because getting good score in JEE, you basic concepts and understanding should be very clear.Give 2 months to the class 11th portion and complete it full-fledged. After that you will be set for class 12th, now start with NCERTs and then move to the standard books.
Divide time equally for every subject or based on your preference.Devote 10-12 hours daily and note that daily means everyday because consistency is the key..you can take 1 days off after 6 days of dedicated studying.
After completing 50% syllabus, start solving previous year JEE question papers and jot down your weak and strong areas and work on it accordingly.
After completing the syllabus,give lot of mock tests honestly and analyze them afterwards.
Be positive during the preparation and take care of your mental and physical health.
Be honest with yourself and give your best everyday.

I hope my answer helps. All the very best for your future endeavors!