An individual applicant who otherwise qualifies for a license for life insurance, health insurance, annuities, nonprofit health service plans, dental plan organizations, or health maintenance organizations is entitled to be examined as provided in this section. Each individual applicant must pass a personal written examination to determine: the competence of the applicant as to life insurance, health insurance, or annuities or to any subdivision of them, including contracts for nonprofit health service plans, vision plans, dental plan organizations, and health maintenance organizations; and the familiarity of the applicant with the applicable laws of the State. Each examination must be graded within 30 days after the date of the examination. An individual applicant who fails an examination may not take another examination until at least 4 days after the date of the last examination that the applicant failed. The Commissioner shall adopt reasonable regulations that specify: the scope, type, conduct, and grading of the written examinations; and the frequency, times, and places in the State where the written examinations will be held.