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Number of ordered pairs in a relation defined by a condition

This type of question, asked 3 times: 29 Jul 2022, 6 Apr 2023, 22 Jan 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    29 Jul 2022

    61
    Let RR be a relation from the set {1,2,3,…,60}\{1,2,3,\ldots,60\} to itself such that R={(a,b):b=pq\mathbf{R = \{(a,b):b = pq}, where p,q≥3p,q \geq 3 are prime numbers }\}. Then, the number of elements in RR is:

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  2. Question 2

    6 Apr 2023

    88
    Let A={1,2,3,4,….10}\mathbf{A = \{ 1,2,3,4,\ldots.10\}} and B={0,1,2,3,4}\mathbf{B = \{ 0,1,2,3,4\}}. The number of elements in the relation R={(a,b)\mathbf{R = \{(a,b)}  ∈A×A:2(a−b)2+3(a−b)∈B}\left. \ \in A \times A:2(a - b)^{2}+ 3(a - b) \in B \right\} is

  3. Question 3

    22 Jan 2026 S2

    53
    The number of elements in the relation R={(x,y)\mathbf{R = \{(x,y)} :  4x2+y2<52,x,y∈Z}\left. \ 4x^{2}+y^{2}< 52,x,y \in Z \right\} is

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