Hello Aspirant

Admission into an Engineering college requires you to have Science (Physics, Chemistry, Math, Biology is not required) in your 11th and 12th grades. Seeing you had all these subjects in your school, you are eligible to appear for the JEE exam. You just make sure you scored 50%+ in your 12th grade, that is one of the eligibility criteria.  They don't mind that Math was your 5th or 6th subject, they just need Math in your core papers.

Getting admission to a good Engineering college depends on the score you get in the JEE Mains and JEE Advance exams.

Here is a link to the Careers360 College predictor that will help you narrow down your choices-

Hope this helps