JEE Main 2026 · 2 Apr · Shift 2 · Mathematics Q21

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MathematicsInteger+4 / -1Question 21 of 75

Let $A=\{2,3,4,5,6\}$ . Let R be a relation on the set $A\times A$ given by $(x,y)\,R\,(z,w)$ if and only if $x$ divides $z$ and $y\le w$ . Then the number of elements in R is ________.

Your answer

Answer and worked solution

Official answer: 120

Count the two parts separately.

Pairs $(x,z)$ with $x\mid z$ in $\{2,\dots,6\}$ : $x=2$ : 3; $x=3$ : 2; $x=4,5,6$ : 1 each. Total 8.
Pairs $(y,w)$ with $y\le w$ : $\binom52+5=15$ .

Total $8\times15=120$ .

Answer: 120

Topics:Relations

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JEE Main 2026 · 2 Apr · Shift 2, Mathematics question 21