The eligibility for Food Inspector (General eligibility) is -

• Graduation in medicine or have a bachelors degree in agriculture, pharmacy, food technology and dairy technology.
• Candidates aged between 18 and 25 years of age are eligible to apply for the post of Food Inspector.

Now the eligibility for UPSC ALL INDIA FOOD INSPECTOR EXAM:

• Graduates in medicine with one year training in food inspection.
• Bachelors degree in science stream with chemistry as a compulsory.
• Bachelor’s degree in Agriculture / Public Health/ Veterinary Science/Dairy Technology/Pharmacy / Food Technology

Thus if you have chemistry as one of the subjects in BCA then you can apply for it. Else you aren't eligible for the examination.

To know more about the career of food inspector visit the link below:

https://www.careers360.com/careers/food-inspector

I hope this answer helps. All the very best for your future endeavors!