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GATE (Graduate Aptitude Test in Engineering) is an all India entrance exam which allows candidates to apply for IITs, NITs, IISc, and a few other applied sciences institutes/universities.
GATE exam can only be given by the candidates with applied science degrees like B.E and B.Tech, to pursue M.Tech and MSc by research, integrated PhD, direct PhD programs.
IIT JAM(Joint Admission test for MSc) is an all India entrance exam which allows candidates to apply for IITs, IISERs, IISc, and NITs.
IIT JAM exam can be given by the candidates with both basic sciences and applied sciences degrees to pursue MSc (Four Semesters), Joint MSc-Ph.D, MSc-M.Tech., MSc-Ph.D Dual Degree & other courses.
IIT JAM syllabus mainly includes topics that candidates usually study in their bachelor’s degree programs.
GATE syllabus has slightly advanced topics in syllabus. GATE syllabus includes some part of the JAM syllabus in addition to some extra advanced topics.
So, it’s upto you, whether your choose IIT JAM or GATE Exam.