JEE Main 2022 · 28 Jul · Shift 1 · Mathematics Q8

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MathematicsSingle correct+4 / -1Question 8 of 90

For $\alpha\in\mathbf N$ , consider a relation R on $\mathbf N$ given by $R=\{(x,y):3x+\alpha y\text{ is a multiple of }7\}$ . The relation R is an equivalence relation if and only if :

\alpha=14

\alpha

is a multiple of 4

4 is the remainder when

\alpha

is divided by 10

4 is the remainder when

\alpha

is divided by 7

Answer and worked solution

Official answer: D

Reflexive needs $(3+\alpha)x\equiv0\pmod7$ for all x, i.e. $\alpha\equiv4\pmod7$ .

Then $3x+\alpha y\equiv3(x-y)$ , which is symmetric and transitive.

(D)

Topics:Relations

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JEE Main 2022 · 28 Jul · Shift 1, Mathematics question 8