The correct answer is option 'A' - i) only.

Explanation:
The International Monetary Fund (IMF) is an international organization that aims to promote global monetary cooperation, secure financial stability, facilitate international trade, promote high employment and sustainable economic growth, and reduce poverty around the world. It consists of 190 member countries and operates under a framework of governance.

The executive board is one of the key components of the IMF's governance structure. It conducts the day-to-day business of the IMF and makes important decisions regarding its policies and operations. However, the statement that the executive board meets once a year is incorrect.

Let's break down the given statements individually:

i) Executive board conducts the business of the IMF:
This statement is true. The executive board is responsible for the management and administration of the IMF's activities. It consists of 24 executive directors who represent the member countries or groups of countries. They are responsible for making decisions on various matters, including financial assistance to member countries, surveillance of global economic developments, and policy discussions.

ii) It meets once in a year:
This statement is incorrect. The executive board of the IMF does not meet annually. In fact, the executive board meets on a regular basis throughout the year to discuss and decide on various issues related to the IMF's mandate. The frequency of meetings may vary depending on the urgency and importance of the matters at hand.

In conclusion, only statement i) is correct, while statement ii) is incorrect. The executive board of the IMF conducts the business of the organization, but it does not meet only once a year.