Masters

Yes you have to give GATE exam for getting admission in M.Tech in Engineering Management. Manipal Institute of Technology, Manipal admits students on the basis of GATE as well as through Manipal Entrance Test.

HiThe syllabus for all entrance exams are given on the web site of a university from where you want to give the test. You can check from CAR JRF Syllabus - AgriGyan. In
I know about LPU an ICAR recognised university of repute. If you check from their website you will get the syllabus and the paper pattern also for the entrance test named LPU NEST. Log in to the sites of some good colleges to check the academic benefits it offers which might suit you. All the best !

Hi, Yes, you can easily apply for Ph.D. as you have completed your Masters degree. I would suggest you few top universities for Ph.D. in India. And the link I am mentioning all will give you deep insight to all your queries regarding edibility criteria, exams any conducted, fees and which is the best specialisation to do Ph.D. and universities to pursue. https://www.shiksha.com/ph-d-chp.