To pursue M.Tech, NITs and IITs are the best institutes and for that Gate exam is compulsory to give so you can also apply for the same as registration process get started in the month of Aug-Sep.

Also, there are other state and private college/university level entrances aas well which you can apply for as the eligibility and admission criteria vary accordingly.

To know more about Gate exam, you can go through the below link -

https://engineering.careers360.com/articles/gate

Good Luck!!!