Each applicant for an office or employment in such classified service, except those exempted by or as provided by this part, shall be subjected to a test, which shall be public and competitive, subject to limitations specified in the rules of the board as to residence, age, health, habits and moral character. Such tests shall be practical in their character and shall relate to those matters which will fairly disclose the relative capacity of the persons tested to discharge the duties of the position to which they seek to be appointed, and may include tests of mental qualification, of physical qualification and health and, when appropriate, of manual or technical skill. No questions in any test shall relate to political or religious opinions or affiliations. When a training school has been established in any institution, the pupils thereof may be classified, under the rules of the commission, as apprentices, subject to promotion to higher grades in the service as provided in this part. The rating of apprentices, unskilled laborers and domestic servants need not relate to more than capacity and fitness for labor, habits of industry and sobriety and honesty. The board shall control all tests and may, whenever a test is to be made, designate a suitable number of persons to be examiners or the commissioners may, at any time, act as such examiners without appointing other examiners. Notice of the time, place and general scope of each test shall be given by the board, by ample publication for three weeks preceding such test, and such notice shall also be posted by such board in a conspicuous place in its office for three weeks before such test. Such further written or printed notice of tests may be given as the board prescribes. Application for tests shall be made in writing, to the board, on a form prescribed by the board, not less than forty-eight hours before the test is to take place. The board may refuse to certify an applicant who is found to lack any preliminary requirement, established by its rules, for the test or position for which he applies, or who is found physically unfit to perform the duties attaching to such position, or who is addicted to the use of intoxicating beverages to excess, or who has been guilty of a crime or of infamous or notoriously disgraceful conduct, or who has, within two years, 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 application or in his test or in securing his eligibility to appointment.