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Regular, private, distance all three modes are valid if the university is approved by UGC. Check out the detailed eligibility below:
Candidates who have secured at least 55% marks in their Master's degree exams (in streams such as humanities, social science, electronic science, computer science & applications, etc.). From a UGC recognised college/ university, fulfill UGC NET 2018 eligibility criteria. It may be noted that a minimum percentage required to meet UGC NET eligibility criteria for candidates belonging to SC/ ST/ OBC/ PWD categories is 50%. Candidates who are appearing or awaiting results for their final year examination of Master's degree are also eligible to appear for UGC NET 2018. However, such candidates will be admitted provisionally and will be considered for JRF and Assistant Professor or Assistant Professor only when they pass their Masters exams with a required percentage. Such candidates must complete their PG degree examination within 2-years from the date of NET result with required percentage of marks, failing which they shall be treated as disqualified, informs the official website.
Note for Ph.D degree holders: Ph.D degree holders whose Masters exams completed on September 19, 1991 (regardless of the result declaration date) will be eligible for a relaxation of 5% marks in the aggregate. This means that the minimum percentage required to meet UGC NET 2018 eligibility criteria for such candidates will be 50% instead of 55%.

Both are important, go for CEH first.
Starting from the point of view, Hacking doesn't require eligibility of academics. Hacking is just a skill which requires, coding knowledge, network knowledge, server-side scripting knowledge, computer hardware knowledge and testing knowledge. Coming to the part, if you saw the articles, the children are around 5 - 11 years of age are hacking networks, finding zero-day flaws in software, etc. So this shows hacking doesn't require any academic courses. Learning hacking through any certification such as EC - Council CEH, (ISC)2s CISSP, CISA and CISM from ISACA and OSCP from Offensive Security will improve the professional skills of hacking.