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Is every reversible process quasi static? If not, what are some examples?

If process is irreversible then it doesn't need to be non quasi-static, I understand that. (eg. free expansion of the gas)

Can irreversible process be quasi static? If so what are some examples?

When is the formula for calculating entropy change applicable (dS=dQ/T)? Is it for reversible or it can also be for irreversible quasi-static (if they exists)?