Consider two sets $\mathrm{A}=\{x \in \mathrm{Z}:|(|x-3|-3)| \leq 1\}$ and

$\mathrm{B}=\left\{x \in \mathbb{R}-\{1,2\}: \frac{(x-2)(x-4)}{x-1} \log _e(|x-2|)=0\right\}$. Then the number of

onto functions $f: \mathrm{A} \rightarrow \mathrm{B}$ is equal to :

Let $\mathrm{A}=\{0,1,2, \ldots, 9\}$. Let R be a relation on A defined by $(x, y) \in \mathrm{R}$ if and only if $|x-y|$ is a multiple of 3.

Given below are two statements :

Statement I : $n(\mathrm{R})=36$.

Statement II : R is an equivalence relation.

In the light of the above statements, choose the correct answer from the options given below :

Let $\mathrm{A}=\{-2,-1,0,1,2,3,4\}$. Let R be a relation on A defined by $x \mathrm{R} y$ if and only if $2 x+y \leqslant 2$. Let $l$ be the number of elements in R . Let m and n be the minimum number of elements required to be added in R to make it reflexive and symmetric relations respectively. Then $\mathrm{l}+\mathrm{m}+\mathrm{n}$ is equal to :

The number of elements in the relation $\mathrm{R}=\left\{(x, y): 4 x^2+y^2<52, x, y \in \mathbf{Z}\right\}$ is