Before a child may become eligible for adoption support under this act, it shall be necessary that:

(a) The child shall be or have been a child hard to place in adoption due to attitudes of society toward his: Age; racial or ethnic background; mental, emotional or physical handicap; or membership in a sibling group; and

(b) The child shall have resided in a foster home or child-care institution or, in the judgment of the secretary, is both eligible for, and likely to be placed in, either a foster home or institution.