(a) one secretary of each state department or division, temporary state commission or other state officer authorized by law to appoint a secretary;

(b) the deputies of principal executive officers authorized by law to act generally for and in place of their principals;

(c) one secretary of each municipal board or commission authorized by law to appoint a secretary;

(d) one clerk and one deputy clerk if authorized by law, of each court, and one clerk of each elective judicial officer, and also one deputy clerk, if authorized by law, of any justice of the supreme court;

(e) all other subordinate offices or positions for the filling of which competitive or non-competitive examination may be found to be not practicable. Not more than one appointment shall be made to or under the title of any office or position placed in the exempt class pursuant to the provisions of this paragraph, unless a different number is specifically prescribed in the rules. 2. No office or position shall be deemed to be in the exempt class unless it is specifically named in such class in the rules. Upon the occurrence of a vacancy in any position in the exempt class, the state or municipal civil service commission having jurisdiction shall study and evaluate such position and, within four months after the occurrence of such vacancy, shall determine whether such position, as then constituted, is properly classified in the exempt class. Pending such determination, said position shall not be filled, except on a temporary basis.