Eligibility for original appointment or promotion to vacancies in positions in the classified service occurring after August 22, 1973, shall be determined by the personnel board. The personnel board shall conduct such examinations as shall fairly test the abilities and aptitudes of the applicants with respect to the duties to be performed. Applicants who pass the test and otherwise qualify for original appointment or promotion, as the case may be, shall be placed on the appropriate eligible list for the vacancy. The board may refuse to examine, or after examination refuse to certify the name of anyone who is found to lack any of the established qualification requirements for the position for which he or she applies or who is physically so disabled as to be unfit to perform duties of the position to which he or she seeks appointment, or who has been convicted of or is under indictment for any crime involving moral turpitude or who has been guilty of any infamous or disgraceful conduct or who has been dismissed from the public service for delinquency or misconduct or who has intentionally made a false statement of any material fact or practiced or attempted to practice any deception or fraud in his or her application, or in his or her examination.