The correct option for the sentence "Mr. Thomas talked .... about the successes of his institute in the past year" is C. at great length. Let's break down why this is the correct choice and analyze the other options. Explanation of the Correct Answer (C. at great length)

1. Understanding the Phrase: The phrase "at great length" is an idiomatic expression in English that means to speak or write in a detailed and extensive manner. It suggests that Mr. Thomas provided a lot of information and elaborated thoroughly on the successes of his institute.
2. Preposition Usage: The preposition "at" is commonly used with the phrase "great length." In English, certain phrases are fixed and do not change. "At great length" is one of those phrases, and it is the correct collocation.
3. Contextual Fit: The context of the sentence indicates that Mr. Thomas is discussing the successes of his institute, which implies a need for detail and depth in his discussion. Therefore, "at great length" fits perfectly as it conveys that he spoke extensively about the topic.

Why the Other Options Are Incorrect

• A. at a great length: This option is very close to being correct, but it is slightly less common than "at great length." The inclusion of "a" makes it sound awkward in this context. While it is grammatically correct, it is not the preferred idiomatic expression.
• B. for great length: This option is incorrect because "for great length" is not a standard English expression. The preposition "for" does not work in this context. We do not use "for" to describe the manner in which someone talks about a topic. Instead, we use "at" to indicate the extent of the discussion.
• D. for a great length: Similar to option B, this phrase is also incorrect. The use of "for" is inappropriate here, and adding "a" does not make it correct. The phrase does not convey the intended meaning of discussing something in detail.

Summary of Key Points

• Correct Phrase: "At great length" is the idiomatic expression used to indicate extensive discussion.
• Preposition Importance: The choice of preposition is crucial; "at" is the correct preposition in this context.
• Common Pitfalls: Avoid using "for" in this context, as it does not convey the same meaning and is not idiomatic.
• Contextual Relevance: The context of discussing successes implies a need for detailed elaboration, which "at great length" effectively communicates.

Revision Summary

• The correct answer is C. at great length.
• "At great length" means to speak in detail or extensively.
• "For great length" and "for a great length" are incorrect due to improper preposition use.
• "At a great length" is less common but still grammatically acceptable; however, "at great length" is preferred.