1
JEE Main 2026 (Online) 8th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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

I. The number of elements in R is 17

II. R is an equivalence relation

A

Only I is true

B

Only II is true

C

Both I and II are true

D

Neither I nor II is true

2
JEE Main 2026 (Online) 24th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $R$ be a relation defined on the set $\{1,2,3,4\} \times\{1,2,3,4\}$ by

$$ \mathrm{R}=\{((a, b),(c, d)): 2 a+3 b=3 c+4 d\} . $$

Then the number of elements in R is

A

6

B

15

C

12

D

18

3
JEE Main 2026 (Online) 23rd January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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 :

A

32

B

81

C

79

D

62

4
JEE Main 2026 (Online) 23rd January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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 :

A

Statement I is correct but Statement II is incorrect

B

Both Statement I and Statement II are correct

C

Both Statement I and Statement II are incorrect

D

Statement I is incorrect but Statement II is correct

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