JEE Main 2026 · 8 Apr · Shift 2 · Mathematics Q1

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MathematicsSingle correct+4 / -1Question 1 of 75

Consider the relation R on the set $\{-2,-1,0,1,2\}$ defined by $(a,b)\in R$ if and only if $1+ab>0$ . Then, among the statements :

I. The number of elements in R is 17

II. R is an equivalence relation

Only I is true

Only II is true

Both I and II are true

Neither I nor II is true

Answer and worked solution

Official answer: A

Count. Of the 25 pairs, $1+ab\le0$ only when a and b are non-zero with opposite signs: $a\in\{-2,-1\}$ , $b\in\{1,2\}$ or the reverse, 8 pairs. So R has 17 elements: I is true.

Equivalence? R is reflexive ( $1+a^2>0$ ) and symmetric, but not transitive: $(2,0),(0,-2)\in R$ while $1+2(-2)<0$ . II is false.

(A)

Topics:Relations

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JEE Main 2026 · 8 Apr · Shift 2, Mathematics question 1