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Why do we say "Do you mind if I open the window" when we should say "Would you mind if I opened the window" or "will you mind if I open the window" ? "Do you mind if I open the window" does not seem grammatically correct as far as tense is concerned.
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Do you mind if I open the window? (both mind and open are in the present tense so I don't see why you think the tenses there are wrong)

I don't see much difference between do you mind and would you mind? Possibly would you mind is slightly more polite but perhaps not.
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Debpriya De"Do you mind if I open the window" ... "Would you mind if I opened the window"
Both of these are set phrases. Don't expect them to follow the exact logic of the grammatical system of English. Just learn them as set phrases. Of the two, the one with "would" is more polite, but only very slightly so. ("Will you mind ...?" is not used.)

CJ