The formula for calculating gate score out of 1000 is as follows:
S=S(q)+[S(t)-S(q)]*[{M-M(q)}/{M(t)-M(q)}]

S= Gate score (normalised) of a candidate
M= Marks obtained by candidates in a paper
M(q)=Qualifying marks of general category candidate in the paper
M(t)=Marks of top 0.1% or 10(whichever is higher) candidates in the paper
S(t)= Gate score assigned to M(t)
S(q)=Gate score assigned to M(q)

M(q) is normally 25(out to 100) or u+s whichever is higher ,where u is the mean of marks in a paper and s is the standard deviation.

For any other details refer to  the following link:
https://engineering.careers360.com/articles/gate-normalisation-process-how-scores-are-calculated

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GATE score is valid for 3 Years.You can refer the link to know how the scores are calculated out of 1000 in the below link.

https://engineering.careers360.com/articles/gate-normalisation-process-how-scores-are-calculated