By a hair's breadth means by a very small distance or amount. This answer is correct because the expression has a fixed figurative meaning in English. In an SSC idiom question, students should match the whole phrase with its accepted meaning rather than translate each word separately.

• Classroom example: By a hair's breadth can refer to a situation involving by a very small distance or amount.
• Story example: A writer may use By a hair's breadth when describing a situation involving by a very small distance or amount.
• Exam example: When a sentence contains By a hair's breadth, choose the meaning “by a very small distance or amount.”