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Yes, you can apply. The eligibility criteria as under:
Eligibility :-
(1) For Maharashtra Candidature Candidates, All India candidature Candidates, Jammu and Kashmir Migrant candidature candidates. (I) The candidate should be an Indian National;
(ii) Passed minimum three year duration Bachelor's Degree awarded by University recognized by University Grants Commission or Association of Indian Universities in any discipline with at least 50% marks in aggregate or equivalent (at least 45% in case of candidates of backward class categories and Persons with disability belonging to Maharashtra State only);(iii) Studied Mathematics as one of the subjects at (10+2) level or at Graduate level examination;
(iv) For Direct second year admissions, the candidate should have passed Bachelor Degree in Computer Applications or Science (Information Technology or Computer Science).(v) Obtained score in MAH MCA CET.

JB,
You cannot apply for TGT exam. The eligibility criteria are as under:-
1. Four years integrated degree course of Regional College of Education of NCERT in the concerned subject with at least 50% marks in aggregate or Bachelors Degree with at least 50% marks in the concerned subject/combination of subject and in aggregate. The elective subjects and languages in the combination of subjects.
2. B.Ed or equivalent degree from a recognised university.
3. Pass in the Central Teacher Eligibility Test CTET Paper-II, conducted by CBSE in accordance with the Guidelines framed by the NCTE for the purpose.
4. Proficiency in teaching in Hindi and English medium. Desirable Qualification: Knowledge of Computer Application.