In this paper we study the connections between right quasi-duo rings and 2-primal rings, including several counterexamples for answers to some questions that occur naturally in the process. Actually we concern following three questions and modified ones: (1) Are right quasi-duo rings 2-primal$ulcorner$, (2) Are formal power series rings over weakly right duo rings also weakly right duoulcorner and (3) Are 2-primal rings right quasi-duoulcorner Moreover we consider some conditions under which the answers of them may be affirmative, obtaining several results which are related to the questions.