In this English grammar sentence improvement question, you must select the correct preposition to replace the bracketed word in "My brother is indifferent (about) whatever I say." so that the sentence follows natural standard usage.

Introduction / Context:
This question tests your knowledge of correct preposition usage with adjectives in English. Certain adjectives are followed by fixed prepositions, and using the wrong one makes the sentence sound unnatural or ungrammatical. The adjective in focus here is "indifferent", and the sentence describes how the brother reacts to whatever the speaker says. Your task is to choose the preposition that is normally used after "indifferent" in standard English.

Given Data / Assumptions:
- The original sentence is: "My brother is indifferent (about) whatever I say."
- The options are "in", "of", "to", and "No improvement".
- The idea of the sentence is that the brother does not care about or is unaffected by what the speaker says.

Concept / Approach:
In English, some adjective and preposition combinations are fixed or very common, such as "fond of", "good at", and "interested in". The adjective "indifferent" is usually followed by "to" when we want to say that someone does not care about or is not concerned with something. Phrases like "indifferent to criticism" or "indifferent to the outcome" are standard. Therefore, we should search for the preposition that maintains this established pattern.

Step-by-Step Solution:
Step 1: Identify the adjective "indifferent" in the sentence. Step 2: Recall common collocations: English typically uses "indifferent to something". Step 3: Check option "in". The phrase "indifferent in whatever I say" sounds unnatural and is not a standard combination. Step 4: Check option "of". "Indifferent of whatever I say" is also not standard usage. Step 5: Check option "to". "Indifferent to whatever I say" is the correct and idiomatic collocation. Step 6: Recognise that "No improvement" is incorrect because "indifferent about whatever I say" is not the most natural preposition choice here.

Verification / Alternative check:
If you consult common examples, you will find phrases like "indifferent to pain", "indifferent to results", or "indifferent to public opinion". These show that "to" is the usual preposition after "indifferent". The idea is that something does not affect or concern the person. Therefore, "My brother is indifferent to whatever I say" correctly conveys that he does not care about or react to the speaker's words. The other prepositions rarely occur in this pattern and sound awkward.

Why Other Options Are Wrong:
"In" is wrong because "indifferent in" is not standard and does not convey the intended meaning. "Of" is wrong because it usually follows adjectives like "fond of" or "aware of", but not "indifferent". "No improvement" is wrong because "indifferent about" is weaker and less idiomatic than "indifferent to" in this context. Examinations usually test these fixed adjective–preposition patterns explicitly.

Common Pitfalls:
Learners sometimes treat prepositions as freely interchangeable, assuming that if the meaning is roughly understandable, it is acceptable. However, native usage depends heavily on collocations. A good way to avoid errors is to read more examples and note which preposition follows which adjective. Over time, patterns like "indifferent to" become automatic and help you answer such questions quickly.

Final Answer:
The correct preposition is to, so the sentence should read: "My brother is indifferent to whatever I say."