Hi, the query that you have mentioned is unclear as to what your doubt is. Do you wish to do your masters in mechanical engineering or do you wish to pursue your bachelors degree in mechanical. For your bachelors degree you can give your state level CET for getting into colleges in your state or JEE for getting into any college in the country. The dates vary according to your exam that you choose. For masters you will have to give GATE exam. The exam dates for GATE are February 5, 6, 12 and 13. If you still have doubts feel free to comment. Hope this helps.