1) The committee have decided to nominate Mrs. Saxena as the President.
2) The committee has decided to nominate Mrs. Saxena as the President.
3) The committees has decided to nominate Mrs. Saxena as the President.
4) The committee is decide to nominate Mrs. Saxena as the President.
5) None of these
Rule ⇒ When the group acts as a unit the verb should be singular. Committee is the collective noun, thus, verb used will be singular i.e. has.