A legislation that confers on the executive or administrative authority an unguided and uncontrolled discretionary power in the matter of the application of law violates which one of the following Articles of the Constitution of India?

The correct option is Article 14.

Step-by-Step Explanation:

1. Understanding Article 14 of the Constitution of India:
Article 14 guarantees the "Right to Equality." It provides that the State shall not deny to any person equality before the law or the equal protection of the laws within the territory of India.

2. The Concept of "Rule of Law" and Arbitrary Power:
Article 14 embodies the principle of the Rule of Law. A fundamental aspect of the Rule of Law is the absence of arbitrary or uncontrolled power. If a piece of legislation grants unguided, uncanalized, or uncontrolled discretionary power to an executive or administrative authority, it allows the authority to apply the law arbitrarily or to discriminate between persons without any clear policy or intelligible differentia.

3. Why such Legislation Violates Article 14:
The Supreme Court of India has repeatedly held that equality and arbitrariness are sworn enemies. Where an act confers unguided discretion, it enables potential abuse of power and unequal treatment, thereby directly violating the guarantee of equality under Article 14.

4. Overview of Other Mentioned Articles:
• Article 28: Relates to freedom as to attendance at religious instruction or religious worship in certain educational institutions.
• Article 32: Relates to remedies for enforcement of Fundamental Rights (Right to Constitutional Remedies).
• Article 44: Relates to the Directive Principle for a Uniform Civil Code for the citizens.

Therefore, conferring unguided and uncontrolled discretionary power violates Article 14 of the Constitution of India.