BCA Eligibility

CBI recruits candidates through direct recruitment, deputation, promotion by seniority or through Limited Departmental Competitive Examination. All direct recruitment of Group C posts for sub-inspectors, constables and lower division clerk are made through Staff Selection Commission (SSC). Procedure to join in CBI as sub inspector:
Sub inspectors are recruited through SSC's Combined Graduate Level Examination (CGLE), followed by medical examination and personal interview. To join IB, you have to apply for the Combined Graduate Preliminary examination (CGPE). It's nothing but CGLE only. This exam is conducted by the SSC every year. The eligibility required for this examination is given below (at last in the answer). Education qualification:
To apply for this examination, a candidate should be a graduate in any discipline from a recognized university. Those appear in the final year examination are also eligible. Age limit:
For the Intelligence Bureau (IB), candidate's age should be between 20 to 27 years. There is relaxation in age for the reserved category candidates like scheduled castes/ scheduled tribes, etc.

Yes, commerce students can pursue BCA even after being from non-mathematical background. Many universities provide admission to such students/candidates. Just look for that university and college, as you've already studied computer Science in your +2, BCA will be relatively easy for you. If you want to learn programming languages which you will be studying in your BCA course then you can check out this app which is specially designed and developed for BCA students. It has programs and assignments of languages like C, C+ and Java with their outputs. You'll be studying these languages in your 3 years of BCA. https://play.google.com/store/apps/details?id=technark.bca_courprogramming.