The board of adjustment, subject to appropriate conditions and safeguards as provided by the zoning ordinance or the ordinance establishing the board of adjustment, if there be such, shall hear and decide:

(1) Applications for conditional uses or other permits when the zoning ordinance sets forth the specific uses to be made subject to conditional use permits and establishes criteria for determining the conditions to be imposed;

(2) Application for variances from the terms of the zoning ordinance: PROVIDED, That any variance granted shall be subject to such conditions as will assure that the adjustment thereby authorized shall not constitute a grant of special privilege inconsistent with the limitations upon other properties in the vicinity and zone in which subject property is situated, and that the following circumstances are found to apply;

(a) because of special circumstances applicable to subject property, including size, shape, topography, location or surroundings, the strict application of the zoning ordinance is found to deprive subject property of rights and privileges enjoyed by other properties in the vicinity and under identical zone classification;

(b) that the granting of the variance will not be materially detrimental to the public welfare or injurious to the property or improvements in the vicinity and zone in which subject property is situated.

(3) Appeals, where it is alleged by the applicant that there is error in any order, requirement, permit, decision, or determination made by an administrative official in the administration or enforcement of this chapter or any ordinance adopted pursuant to it.