Hello Aspirant,
If we go through the analysis of previous year's GATE score Vs College allotment than according to the GATE 2021 score mentioned by you in the query, you have very low chances in IIT Bombay with design specialization, because last year the closing cut-off for IIT Bombay was 844 for design specialization for last round.
You can check out previous year's cut-offs from the link given below :-
https://engineering.careers360.com/articles/gate-cutoff-for-nit-warangal
Note that the above prediction is made on the basis of latest cut-offs and the cut-offs are bound to change every year depending upon various factors such as the number of candidates appearing in an examination, the number of candidates qualifying an examination, difficulty level of the paper, and so on.
To have a list of all those colleges which you can get based upon your GATE 2021 Score and category you can use GATE College Predictor :-
https://engineering.careers360.com/gate-college-predictor?icn=QnA&ici=qna_answer
You can also check out the GATE qualifying cut-off for GATE 2021 from the link given below :-
https://engineering.careers360.com/articles/gate-cutoff
I hope this information helps you.
Good Luck!!
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