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JEE MainMathematicsSets and Relations

Let A = 1, 2, 3, , 20 . A relation R is defined on A such that (x, y) R if and only if xy is a perfect square. The total number of ordered pairs in R is :

Options

  1. A20
  2. B42
  3. C33
  4. D22

Correct answer

B. 42

Step-by-step solution

The relation R is an equivalence relation because xy being a perfect square means x and y have the same square-free part. We can partition the set A = 1, 2, 3, , 20 into equivalence classes based on their square-free parts: Class 1 (square-free part 1): 1, 4, 9, 16 (4 elements) Class 2 (square-free part 2): 2, 8, 18 (3 elements) Class 3 (square-free part 3): 3, 12 (2 elements) Class 4 (square-free part 5): 5, 20 (2 elements) The remaining elements 6, 7, 10, 11, 13, 14, 15, 17, 19 each form a class of 1 element (9 c

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