GATE

Hello Harshini,
It is not important as if you are getting a job then you should get the job but I would say you if you are GATE qualified then one more degree is added to your qualification which gives you more respect in front of your company. And you can a better package than the one you were getting previously.

Obviously, GATE exam is tougher than JEE Mains exam. JEE Mains involves the concepts and problems at the basic level (11th &12th NCERT syllabus), but JEE Advanced will be tougher.
In case of GATE exam, the questions will be based on the concepts from engineering level (from your B.Tech syllabus). So it will be very difficult when compared to JEE Mains.
JEE Advanced will be tough for a candidate who aspires to become an engineer.
All the best.

After your M.Tech, your entry cadre will be that of Assistant Professor. You can make a career progression to Associate Professor and Professor later on with experience if you have a Ph.D.

Hello Parth,
These two coaching institutes are best for GATE preparation:
1. The GATE Academy, Ahmedabad
No. 323, 3rd Floor, Sunrise Mall, Near Manasi Circle, Vastrapur, Ahmedabad, Gujarat 380015
2. Ice GATE Insitute
201, Sunrise Mall, 1st Floor, Near Mansi Circle, Vastrapur, Ahmedabad, Gujarat 380015
All the best.

Hello Lovely,
Please follow the link provided below for complete details about the books according to your branch form which you have done your B.Tech:
https://www.shiksha.com/engineering/articles/gate-books-blogId-21817