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Number of one-one functions between two sets found from conditions

This type of question, asked 4 times: 2021 Paper 4, 8 Apr 2024, 9 Apr 2024, 4 Apr 2025. All 4 questions below, oldest first.

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  1. Question 1

    2021 Paper 4

    66
    Let xx denote the total number of one-one functions from a set AA with 3 elements to a set BB with 5 elements and yy denote the total number of one-one functions from the set AA to the set A×BA\times B. Then:

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  2. Question 2

    8 Apr 2024

    74
    Let [t] be the greatest integer less than or equal to t. Let A be the set of all prime factors of 2310 and f:A→Zf:A \rightarrow Z be the function f(x)=[log⁡2(x2+[x35])]f(x) =\left\lbrack \log_{2}\left( x^{2}+\left\lbrack \frac{x^{3}}{5} \right\rbrack \right) \right\rbrack. The number of one-to-one functions from AA to the range of ff is:

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  3. Question 3

    9 Apr 2024

    175
    Let A={(x,y):2x+3y=23,x,y∈N}\mathbf{A = \{(x,y):2x + 3y = 23,x,y \in N\}} and B={x:(x,y)∈A}\mathbf{B = \{ x:(x,y) \in A\}}. Then the number of one-one functions from AA to BB is equal to

  4. Question 4

    4 Apr 2025

    52
    Consider the sets A={(x,y)∈R×R:x2+y2=25}A =\left\{ (x,y) \in\mathbb{R}\times\mathbb{R}:x^{2}+y^{2}= 25 \right\}, B={(x,y)∈R×R:x2+9y2=144},C={(x,y)B =\left\{ (x,y) \in\mathbb{R}\times\mathbb{R}:x^{2}+ 9y^{2}= 144 \right\}\mathbf{,C = \{(x,y)}  ∈Z×Z:x2+y2≤4}\left. \ \in\mathbb{Z}\times\mathbb{Z}:x^{2}+y^{2}\leq 4 \right\}, and D=A∩BD = A \cap B. The total number of one-one functions from the set DD to the set C is:

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