I want to know that doing M.Tech from a private college without giving the GATE exam is beneficial and are there such colleges in Kolkata?

You can go for MTech without GATE from a college giving you the best academic benefits then you can go for a pvt college also. A lot depends upon your score also. So browse some good college sites like SRM, LPU, RV etc to get the best

I think you should clear GATE exam get enrollment in top university or any government college. And if you are looking for some private engineering colleges so I will recommend you to go with shiksha's college predictor tool. With this help you will get some good & reputed private engineering college