GATE

You can check the below mentioned college predictor: https://www.shiksha.com/engineering/course/m-tech-shri-guru-gobind-singhji-institute-of-engineering-and-technology-sggsie-t-nanded-193366

GATE is examination for M.Tech studies in India. Most of universities abroad use GRE score for admission in their MS program. You may plan to appear in both GATE & GRE for wider choices for doing postgraduate degree in Mechanical engineering after B.Tech.

Both are competitive exam, but type of questions are different. GATE questions are purely technical and CAT is management type.

No, you can write GATE examination either in your final year or once you've completed your graduation degree. It is usually held in the month of February once in year. So, you can give GATE exam in February 2018 or later. Not in 2017. For cutoffs and colleges, look up in counselling and MBA heading of https://shiksha.com.

GATEFORUM, TIME and Career Launcher are the best coaching centres in Ahmedabad for GATE.

I would recommend, GK Publishers or The Pearson Guide to GATE.

You may refer GK publication book for GATE exam. But, it is suggested to read Ankur Gupta's note for GATE CSE preparation.

You can refer to Willey acing book.

It depends upon the highest ranker of the GATE, generally it is around 30 to 35 marks for open or general category.