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Counting one-one functions satisfying given conditions

This type of question, asked 2 times: 5 Apr 2024, 5 Apr 2026 S1. All 2 questions below, oldest first.

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  1. Question 1

    5 Apr 2024

    67
    Let A={1,3,7,9,11}\mathbf{A = \{ 1,3,7,9,11\}} and B={2,4,5,7,8,10,12}\mathbf{B = \{ 2,4,5,7,8,10,12\}}. Then the total number of one-one maps f:A→Bf:A \rightarrow B, such that f(a)+f(c)=14f(a) + f(c) = 14, is:

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  2. Question 2

    5 Apr 2026 S1

    71
    Let A={1,2,3,4,5,6}A = \{ 1,2,3,4,5,6\}. The number of one-one functions f:A→Af:A \rightarrow A such that f(1)≥3,f(3)≤4f(1) \geq 3,f(3) \leq 4 and f(2)+f(3)=5f(2) + f(3) = 5, is ____\_\_\_\_ .