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Sure, you can sit for both exams. As minimum graduation percentage eligibility for CAT is 50%.

The following link is to the entrance form: http://pgexam.puchd.ac.in/

Since you have varied interests, you should apply for the UPSC exams. UPSC covers many subjects and you can opt for subjects which fit your interests. Regards.

Hello,
If you wish to appear in UGC NET Exam, then you must require to check the essential qualification and age limit criteria as given below:
Post-graduation with a minimum of 55% marks (50% for SC/ST/PwD/OBC). Candidates who have appeared for the last year's examination of the post-graduation and waiting for the results are also eligible to appear in UGC NET Exam. For JRF (Junior Research Fellowship), age limit is 30 years. Candidates can appear in UGC NET Exam for Lectureship as many time as they want. The Central Board of Secondary Education has announced the notification for conducting the UGC NET 2018 Exam.

The syllabus will be provided to you, once the session start. So, you need to wait till that time.