Yes, Mam, your son is eligible for Karnataka Common Entrance Test (KCET). As per the eligibility requirements:

• The applicant should be a citizen of India.
• The applicant should have passed the 12th examination or equivalent.
• The applicant should have physics and maths subjects in his 12th qualifying examinations with any one of the Chemistry/Biotechnology/Biology/Electronics/Computer with additional subject English.
• The candidate passed from Karnataka State Open University(KSOU) are not eligible.

Moreover, there're certain codes to follow and you fall in the code:

• In which, the candidate should have passed 12th within the state of Karnataka from an educational institutional run or recognized by Karnataka state government.
• Either of the parents of the candidate should have studied in Karnataka for about 7 years.

 For admission the documents will be required:

• 10th standard mark sheet
• 12th standard mark sheet
• For claiming reservation benefits, must have Caste income certificate issued by concerned Tehsildar for SC/ST.
• Must have study certificate of either of the parents studying for 7 years by the head of the institution where they studied.
• Passing certificate of 11th and 12th of the candidate by the head of the institution.

I hope that'll help you, Best of luck to your son for his further career prospects.