Select the most appropriate option that can substitute the underlined segment in the given sentence. If there is no need to substitute it, select ‘No substitution required’.
I had to write a letter of mistake to my father for the blunder I made.

The correct answer is apology.

Explanation:

In the given sentence, the phrase letter of mistake is contextually and idiomatically incorrect. When a person makes a mistake or a blunder and writes a formal or informal letter expressing regret to seek forgiveness, it is called a letter of apology.

Let's analyze the given options:

1. apology: Means an expression of regret or admitting fault for a mistake. Substituting "letter of mistake" with "letter of apology" makes the sentence grammatically correct and meaningful: "I had to write a letter of apology to my father for the blunder I made."

2. circumstance: Refers to a condition connected to or relevant to an event or action, which does not fit the context of regretting a blunder.

3. gratitude: Means the quality of being thankful, which contradicts the context of committing a blunder.

4. No substitution required: Incorrect because "letter of mistake" is an improper expression in English.

Therefore, the segment letter of mistake should be substituted with apology.