Step 1: Relevant UN Charter provision.
Article 13(1)(a) of the United Nations Charter mandates the General Assembly to initiate studies and make recommendations for encouraging the progressive development of international law and its codification.
Step 2: Exclusion of other provisions.
Articles 10, 21, and 25 relate to general powers, internal procedure, and binding nature of Security Council decisions respectively, not codification of international law.
Step 3: Conclusion.
Therefore, the correct answer is (C) Article 13(1)(a).