Hey Abhishek! 
Gate score for iit's - 
Iit's cutoff for gate is the minimum score required for admission into mtech programmes across various iit's. Candidates who scored equal marks or more than cutoff of marks of gate iit's will be considered for admission into mtech programmes.
In the link below there is a list of the iit cutoff for gate - 
https://engineering.careers360.com/articles/gate-cutoff-for-iits
The other colleges preferebly iitd, iitm,iitk,iitkgp,nitie the cutoff includes - 
General - 750+
Obc- 650+
Sc- 400+
St - 350+
The other mtech colleges include - 
Anna University 
Bits pilani
Cochin university of science and technology
College of engineering trivandrum
Delhi college of engineering
Delhi technical university
Gautam buddha technical university
Sv college of engineering 
Wish you all the best! 
As for psu's - 
Since, the competition is fierce and the number of candidates many, it would be advantageous to have a knowledge of the gate cutoff scores for psu requirement
The gate cutoff for psu requirement are based on many factors like the number of applicants, the number of posts that are vacant, the difficulty level of the gate papers and such. 
Using the link you could also check out the previous years cutoff for psu requirement- 
https://engineering.careers360.com/articles/what-are-gate-scores-for-psu-recruitment
Wish you all the best!

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