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JEE Main202315 Apr 2023Morning ShiftMathematicsSets and RelationsActual

Let A = 1 ,   2 ,   3 ,   4 and R be a relation on the set A × A defined by R = a ,   b ,   c ,   d : 2 a + 3 b = 4 c + 5 d . Then the number of elements in R is _________.

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Step-by-step solution

Given, Set A = 1 , 2 , 3 , 4 And relation on A × A as 2 a + 3 b = 4 c + 5 d Now, Maximum value of 2 a + 3 b = 20 at 4 ,   4 And Minimum value of 4 c + 5 d = 9 at 1 ,   1 So, 4 c + 5 d can be equal to 9 ,   13 ,   14 ,   17 ,   18 ,   19 Now 2 a + 3 b can be 9 if a ,   b = 3 ,   1 ⇒ c ,   d = 1 ,   1 Similarly, 2 a + 3 b can be 13 , if a ,   b = 2 ,   3 ⇒ c ,   d = 2 ,   1 And 2 a + 3 b can be 14 , if a ,   b = 4 , &#160

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