Mathematics · 2022
JEE Main · 28 July 2022, Shift 1 · Q8
For α ∈ N, consider a relation R on N given by R ={(x, y): 3 x+α y is a multiple of 7 }. The relation R is an equivalence relation if and only if:
For $\displaystyle \alpha \in \mathbf{N}$, consider a relation R on $\displaystyle \mathbf{N}$ given by $\displaystyle \mathrm{R}=\{(x, y): 3 x+\alpha y$ is a multiple of $\displaystyle 7 \}$. The relation $\displaystyle R$ is an equivalence relation if and only if :
Official answer
(4)
$\displaystyle 4 \text { is the remainder when } \alpha \text { is divided by } 7$
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JEE Main 2022 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.