For your information the eligibility criteria for CAT is as follows, where it is nowhere mentioned that a students form distance education cannot appear for it same is the case for almost every entrance test
CAT Eligibility
The candidate must hold a Bachelor’s Degree, with at least 50%
marks or equivalent CGPA [45% in case of the candidates belonging to
Scheduled Caste (SC), Scheduled Tribe (ST) and Differently Abled
(DA)categories], awarded by any of the Universities incorporated by an
act of the central or state legislature in India or other educational
institutions established by an act of Parliament or declared to be
deemed as a University under Section 3 of the UGC Act, 1956, or possess
an equivalent qualification recognized by the Ministry of HRD,
Government of India.
The percentage of marks obtained by the candidate in the
bachelor’s degree would be calculated based on the practice followed by
the university/institution from where the candidate has obtained the
degree. In case the candidates are awarded grades/CGPA instead of marks,
the conversion of grades/CGPA to percentage of marks would be based on
the procedure certified by the university/ institution from where they
have obtained the bachelor's degree. In case the university/ institution
does not have any scheme for converting CGPA into equivalent marks, the
equivalence would be established by dividing the candidate’s CGPA by
the maximum possible CGPA and multiplying the result with 100.
or visit the following link CAT Information
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