please give me a strategy to complete my syllabus of class 11by the end of December 2021 ,so i prepare for jee advance 2023 and suggest me some idea howany i must have to study for cracking iit jee as a sc category student.

Start studying 2 subjects each day giving equal time to both like 2 or 3 hours each. How many hours a student can study daily can vary from person to person but whatever time you give, make sure you do it without any disturbance and distractions. Keep your phone away unless absolutely necessary while studying. For focused study with concentration and efficiency you need:
1. A systematic schedule
2. Proper study techniques
3. Repeated revision
4. Enough practice
5. Use mind maps to recover easily from memory
6. Relaxation techniques

You will definitely be able to complete your class 11th course by December if you follow these tips. Now coming to jee mains and advanced, both have majorly same course but different patterns. I will attach the links below to make you familiar with both exams completely.

In jee mains, 45% syllabus is from class 11 and 55% from class 12. So, while studying for your class 11 you can include some high level problems for each topic to get you prepared for jee mains along with it. Specially in chemistry portion, majority of the questions are from ncert directly, make sure you go through it thoroughly and revise periodically.

https://engineering.careers360.com/articles/jee-main-2022/amp

https://www.google.com/amp/s/engineering.careers360.com/articles/jee-advanced-exam-pattern/amp

Good Luck !