Since you have completed B.Tech with Mechaelectronics and hence you would be in great demand in public - undertakings such as BHEL, ONGC, SAIL, DVC, NTPC etc.
The eligibility criteria for the graduate - engineers in all the Public - undertakings are more or less the same - ie the aspirant has to secure a minimum aggregate of 65 percent and should be freshly passed out. However, in respect of selection of graduate trainee, the aspirants would be required to clear the written test comprising of Mathematial - ability, Reasoning, General knowledge apart from the stream opted by the candidate in the engineering graduation- level. On clearance of the written test, the aspirant would be called for the oral where the intrinsic potential of the candidates are assessed and lastly they have to satisfy Medical - board with respect to Physical fitness. The pattern appears to be tough and a consistent effort would be required to clear the test organised by the Public Undertakings.
Clearing the GATE test with a high percentile, the candidates would be offered two special increments in their basic - pay apart from other perquisties.
Hence it would be boon for you to have an excellent GATE score.
Of course, you can go in for M. Tech in Mechanical and then you can join a Public - undertaking but considering the length of time of three - years for completion of post - graduation, financial benifits on aquistion of this qualification would not be substantial.
Regarding your last query, you need to secure cent percent scores in terms of percentile in order to grab a seat of M.Tech in IIT.