The correct answer is: ambassador.
An ambassador is a person who represents one country in another. They are usually appointed by the head of state of the sending country and are responsible for maintaining relations between the two countries. Ambassadors typically live in the capital city of the receiving country and have an office called an embassy.
In the context of the question, the American ambassador presented his credentials to the President of India. This means that he formally introduced himself and presented his official documents to the President. This is a necessary step in establishing diplomatic relations between two countries.
The other options are incorrect because they do not accurately describe the role of an ambassador. An adviser is someone who gives advice to a person or group. A delegate is someone who is sent to represent a group at a meeting or conference. A representative is someone who is elected to speak for a group of people.