-->>> Yes Off Course.,Your Eligible for the CBI with the 31 years age..,
>> But your are Not Eligible for the General Category because for this Category the Age limit is 21- 27 years only..,
>> If you are a SC/ST Candidate then you can Apply for the CBI....
-->> Here i given clear Eligibility Criteria For the CBI :-
To join as CBI officer you need to appear for Combined Graduate Preliminary Exam conducted by SSC.
>> Candidates should have a graduation from a recognized university.
>> The age limit must be within 21 to 27 for general category.
>> The age limit must be up to 35 years for SC/ST candidates.
>> The age limit must be up to 33 years for OBC candidates.
For General category - 4 attempts.
For SC/ST category - No limit
For OBC category - 7 attempts