In monopoly, if a player owns all of a set of properties but one of the properties is mortgaged, is the rent still doubled for the other properties?
Yes, rent is doubled even if some of the properties are mortgaged.
Rules

It is an advantage to hold all the Title Deed cards in a color-group
(e.g., Boardwalk and Park Place; or Connecticut, Vermont and Oriental
Avenues) because the owner may then charge double rent for
unimproved properties in that color-group. This rule applies to
unmortgaged properties even if another property in that color-group
is mortgaged.