JEE Advanced 2024 — Paper 2 — Question 36

Let $S=\{1,2,3,4,5,6\}$ and $X$ be the set of all relations $R$ from $S$ to $S$ that satisfy both the following properties: i. $\quad \mathrm{R}$ has exactly 6 elements. ii. For each $(a, b) \in R$,we have $|a-b| \geq 2$. Let $Y=\{R \in X$ : The range of $R$ has exactly one element $\}$ and $Z=\{R \in X: R$ is a function from $S$ to $S\}$. Let $n(A)$ denote the number of elements in a set $A$. (There are two questions based on PARAGRAPH "I", the question given below is one of them)

If $n(X)={ }^{m} C_{6}$, then the value of $m$ is $\qquad$