JEE Advanced Mathematics Question (2024) — Solution

Step-by-step solution

\(S=\ 1,2,3,4,5,6\ R: S S\) Number of elements in \(R=6\) and for each \((a, b) R ;|a-b| 2\) \(X \) set of all relation \(R: S S\) If \(a=1, b=3,4,5,6 (4)\) \(a=2, b=4,5,6 (3)\) \(a=3, b=1,5,6 (3)\) \(a=4, b=1,2,6 (3)\) \(a=5, b=1,2,3 (3)\) \(a=6, b=1,2,3,4 (4)\) Total number of ordered pairs \((a, b)\) s.t. \(|a-b| 2 =20\) \( n(X)=\) number of elements in \( X = ^ 20 C_6\) \( m=20\)