Suppose the conclusion of an argument is known to be tautologous. Do you have to do a truth table to know whether it is valid or invalid?
No. If the conclusion is a tautology, that means it is always true, and it is impossible for it to be false. An argument is truth-functionally valid if it is impossible for the premises to be true and the conclusion to be false. If it's impossible for the conclusion to be false, then the argument is automatically valid for that reason.