Can I still prepare for the JEE if I have other commitments, such as extracurricular activities or a part-time job?
I can`t say you can but I will definitely say that you should.
You should participate in activities because its important.
A lot of people ask on Quora or some even message me that whether I should go with a dummy school or a proper school. My best advice for them is to go with a proper school.
I followed it and it is helpful when you are considering success in life and not just JEE.
JEE preparation is one of the most stressful and hectic time in life. Coaching centres always keep you on your toe and bearing such a large amount of pressure at such a young age is not everybody`s cup of tea.
Joining a proper school allows to interact with friends and that keeps you cool in your studies also.
Its very important to not study with stress during that time.
Not only this, participating in activities helps in the growth of right side of brain which is very essential for human body.
I always was and still is a regular participant in activities wherever I get a chance to present my views by either writing or speaking. I never stopped participating in activities like debate, drama, etc because of JEE. I was even the head boy of school in my class 12th so you see I had some other works to do also but I still managed to keep an attendance of approx 75% in both class 11th and 12th.
The only thing you need to learn for this is better time management and trust me, this is one of the only skill that can make you reach places in life if you can master it.
Your studies are your priority, no doubt about that but let me tell you that at the end of the day (even if you become an IIT-ian) and you can`t speak or show your talent in front of a delegation, that knowledge is of no use then.