Who among the following leaders was unanimously elected for a second term as the Secretary General of the United Nations Organisation (UNO), continuing in this top diplomatic post?

Introduction / Context:
The Secretary General of the United Nations Organisation is the head of the UN Secretariat and plays a key role in international diplomacy, peacekeeping, and coordination of UN activities. Secretaries General are usually appointed for fixed terms and may be reappointed for a second term if there is broad support among member states. This question asks which personality listed in the options was unanimously elected for a second term to this important office.

Given Data / Assumptions:

• The position is Secretary General of the United Nations.
• The person in question was unanimously elected for a second term.
• Options are Nelson Mandela, Hillary R Clinton, Jacob Mathew, and Ban Ki-moon.
• We assume standard knowledge of recent UN leadership.

Concept / Approach:
Ban Ki-moon, a diplomat from South Korea, served as the eighth Secretary General of the United Nations. He was first appointed for a term and later unanimously reappointed for a second term by the UN member states. Nelson Mandela was a South African anti apartheid leader and president, not a UN Secretary General. Hillary R Clinton served as United States Secretary of State but never as UN Secretary General. Jacob Mathew is not known as UN Secretary General in standard general knowledge references. Thus, the only name that fits the description is Ban Ki-moon.

Step-by-Step Solution:
Step 1: Consider which of the listed individuals has actually held the role of UN Secretary General. Step 2: Recall that Ban Ki-moon, from South Korea, served as Secretary General and was reappointed for a second term. Step 3: Note that Nelson Mandela, while a global statesman, was president of South Africa and not Secretary General of the UN. Step 4: Recognise that Hillary R Clinton was a senior United States politician and diplomat but did not occupy the UN Secretary General post. Step 5: Conclude that Ban Ki-moon is the correct answer because he was unanimously chosen for a second term.

Verification / Alternative check:
To verify, think of lists of UN Secretaries General in common reference materials, where Ban Ki-moon appears as the successor to Kofi Annan. These lists also mention that he was reappointed after his first term due to broad support from the member states. No such records associate Nelson Mandela, Hillary R Clinton, or Jacob Mathew with this position, confirming that Ban Ki-moon is the only correct choice.

Why Other Options Are Wrong:
Nelson Mandela is celebrated for his leadership against apartheid and his presidency of South Africa but did not serve as UN Secretary General. Hillary R Clinton is an American political leader and former Secretary of State, again not a UN Secretary General. Jacob Mathew does not feature as a UN Secretary General in standard general knowledge sources. Therefore, none of these other options matches the question's requirement.

Common Pitfalls:
A common error is to choose a highly famous global figure such as Nelson Mandela, assuming that international recognition implies leadership of the United Nations. Another mistake is to pick a well known diplomat like Hillary R Clinton without checking the exact office mentioned. To avoid such errors, it is helpful to memorise the names and nationalities of recent UN Secretaries General separately from other world leaders.

Final Answer:
The leader unanimously elected for a second term as UN Secretary General was Ban Ki-moon.