Examine the logical coherence between the following administrative policies and constitutional limitations:
1. Evidence 1: A state university enacts an admissions policy that explicitly denies entry to all applicants solely because they belong to a specific recognized caste. Inference 1: This policy is a direct violation of the prohibitions outlined in Article 15.
2. Evidence 2: A state government creates a specialized welfare fund accessible exclusively to citizens who are classified as socially and educationally backward. Inference 2: This policy is constitutionally valid because socio-economic backwardness is not a prohibited ground of discrimination.
3. Evidence 3: Article 15 prohibits discrimination on grounds 'only' of religion, race, caste, sex, or place of birth. Inference 3: Therefore, a state policy that requires applicants to pass a strict physical fitness test, resulting in a higher rejection rate for women, is inherently unconstitutional.