Choice "C" is correct. Creation of an agency relationship requires the consent of the parties and that the principal be competent (not a minor and not incompetent).
Choice "b" is incorrect. Consideration is not required to create an agency relationship.Choice "d" is incorrect. The agent need not have capacity; only the principal need have capacity.
Choice "a" is incorrect. A writing to establish an agency-principal agreement is generally not needed unless: (i) the agent is to buy/sell land on behalf of the principal and/or (ii) the agency relationship cannot be performed within one year.