Yes, your son will be eligible for JEE exam as It is mandatory for students to have 5 subjects in 12th or qualifying exam.

The 5 subjects for B.Tech/ B.E. are:

1-Language, 2-Physics, 3-Mathematics, 4-Any one of (Chemistry, Biology, Biotechnology, Technical Vocational Subject), 5-Any other subject

If he qualify for JEE he can take admission in engineering colleges but you should try to get admission in top colleges of engineering for better education and placements. Always prefer a college with good placements.

To get admission in top IITs/NITs and IIITs you must have 75% marks in your board exam or you should be in top 20 percentile. For SC/ST you should have 65% marks in your board exam.

You should also consider to take admission in DTU and NSIT they consider JEE Main marks to provide admission but counselling is conducted through JAC Delhi.

There are many top private colleges as well which have good ratings and provide excellent placements. If you want you can apply for these entrance exam as well to keep a good options with you like BITSAT, VIT, SRM, Manipal and Amrita.

You can check the top colleges for engineering below

Government

Indian Institute of Technology Bombay
Indian Institute of Technology Delhi
Indian Institute of Technology, Kanpur
Indian Institute of Technology Kharagpur
Indian Institute of Technology Madras

Private

Amrita School of Engineering, Coimbatore
Birla Institute of Technology and Science, Pilani
VIT University, Vellore
BMS College of Engineering, Bangalore
Manipal Institute of Technology, Manipal

To check the complete list you can referbelow link

https://engineering.careers360.com/colleges/ranking

Good Luck!!