Subjects you need for engineering (and the ones you don't)
Physics and Mathematics are compulsory, Chemistry is nearly always needed, and nothing else is.
The rule
JEE Main requires Physics and Mathematics in Class 12 with Chemistry, Biology, Biotechnology or a technical vocational subject as the third. JEE Advanced, NATA and most state CETs require Physics, Chemistry and Mathematics. Take all three.
Mathematics, not Applied Mathematics
Only Mathematics (041) qualifies. Applied Mathematics (241) does not, for any engineering entrance.
The fifth subject
Computer Science is the common choice and helps with B.Tech CSE, but it is not required. Economics, Physical Education, Engineering Graphics and Biology are all fine. Pick what you will do well in.
What is not needed
Coaching from Class 9, a sixth subject, or dropping English Elective for Core all make no difference to eligibility. Marks do: 75% in Class 12 (or top 20 percentile) for NIT and IIT admission.
Guidance based on the CBSE scheme of studies and public exam bulletins. Confirm rules with your school and the official sources before deciding.