GATE syllabus . and if I want to get psu after mechanical engineering Then what score I needed in Gate. will category has some benefit ? after gate will they hire me or I have to go there?

To get PSUs after qualifying GATE, you need to apply for the companies separately. The application forms will be released by the individual companies and you'll have to fill required details with correct information. To be eligible for PSU Recruitment, you need to meet the minimum required cutoff. But the specific scores for the recruitment will be announced by each company. Some PSU accepts previous year GATE score, but not all. You can check the previous year GATE cutoff scores and ranks of various PSUs so that you can get an idea about it http://engineering.careers360.com/articles/what-are-gate-scores-for-psu-recruitment
Check the PSU recruitment process here http://engineering.careers360.com/articles/psu-recruitment-through-gate