Which of the following Articles of the Constitution of India, provides for the Right of Minorities to establish and administer educational institutions of their own and that the State shall not discriminate in granting aid tosuch educational institutions?

The correct option is Article 30.

Step-by-step Explanation:

1. Understanding the Constitutional Provision:
Article 30 of the Constitution of India deals with the "Right of minorities to establish and administer educational institutions". It is a fundamental right classified under Culture and Educational Rights (Articles 29 and 30).

2. Key Clauses of Article 30:
- Article 30(1): All minorities, whether based on religion or language, shall have the right to establish and administer educational institutions of their choice.
- Article 30(2): The State shall not, in granting aid to educational institutions, discriminate against any educational institution on the ground that it is under the management of a minority, whether based on religion or language.

3. Analyzing the Other Options:
- Article 21: Protects the right to life and personal liberty.
- Article 25: Provides freedom of conscience and free profession, practice, and propagation of religion.
- Article 29: Provides protection of interests of minorities, specifically their right to conserve their distinct language, script, or culture.

Therefore, Article 30 is the specific article that guarantees minorities the right to establish and administer educational institutions and prohibits state discrimination in granting aid to them.