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Hello Abhishek,
Yes, sure you are eligible for JEE examination.
Qualifying Exam: Candidates must qualify their 10+2 or equivalent examination from a recognised board. For admissions into NITs, IIITs and CFTIs, the candidates should have secured 75%.
Subjects: Candidates must have to take minimum 5 subjects in class 12th/equivalent examination.
Passing Marks: There is no prescribed percentage to appear in the examination. Candidates having passing marks can also apply.
Appearing Candidates: If a candidate appears in class 12th or equivalent class in 2019 are also eligible for JEE Mains 2019.
Indeed, you will not able to get a good government college through JEE Mains because of your low percentage in PCM.
Best of luck.

Hello,
You need to understand that Pilot training is governed and regulated by DGCA and it is irrespective of the flying school you choose to train with. For becoming a commercial pilot, there are specific eligibility criteria, which you should first be aware of. This is decided on what subjects have you taken in class 12th. It requires PCM to be a pilot. And, even if you have not opted for the same, then you can appear separately for these subjects and become eligible. Further, you should be aware that you are medically fit to be a pilot, so I would suggest you to visithttp://www.dgca.nic.in/medical/medical-ind.htmandgototheclass2nd examiners tab to find out doctors who will examine you for initial fitness. You can visit any doctorate from the list as per your convenience. Once you are done with Class 2nd medical, find out a suitable flying club for you as per your convenience. All the best.