New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Sets and Relations question

2025 · 4 Apr · Shift 2 · Q26

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Sets and Relations
2025 · 4 Apr · Shift 2 · Q26

Sets and Relations question

2025 · 4 Apr · Shift 2 · Q26

JEE MainMathematicsSets and RelationsMCQ+4 / −1

Let

\mathrm{A}=\{-3,-2,-1,0,1,2,3\}

and R be a relation on A defined by

x \mathrm{R} y

if and only if

2 x-y \in\{0,1\}

. 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

l+\mathrm{m}+\mathrm{n}

is equal to:

A
17
B
18
C
15
D
16

More from Sets and Relations

The number of relations on the set $A = {1, 2, 3}$ , containing at most 6 elements including , which are reflexive and transitive but not symmetric, is .2025 · Numerical
For $n \geq 2$ , let $S_{n}$ denote the set of all subsets of ${1, 2, \dots, n}$ with no two consecutive numbers. For example ${1, 3, 5} \in S_{6}$ , but ${1, 2, 4} \in / S_{6}$ . Then $n (S_{5})$ is equal to 2025 · Numerical
Let A = { ( $α, β$ ) $\in R \times R$ : | $α$ - 1| $\leq 4$ and | $β$ - 5| $\leq 6$ } and B = { ( $α, β$ ) $\in R \times R$ : 16( $α$ - $2)^{2}$ + 9( $β$ - $6)^{2} \leq 144$ }. Then2025 · MCQ
Let A = {0, 1, 2, 3, 4, 5}. Let R be a relation on A defined by (x, y) ∈ R if and only if max{x, y} ∈ {3, 4}. Then among the statements (S1): The number of elements in R is 18, and (S2): The relation R is symmetric but neither reflexive…2025 · MCQ
Let $A = {1, 2, 3, \dots, 10}$ and $B = {\frac{m}{n} : m, n \in A, m < n$ and $gcd (m, n) = 1}$ . Then $n (B)$ is equal to :2025 · MCQ
The number of non-empty equivalence relations on the set ${1, 2, 3}$ is :2025 · MCQ
Let $A = {1, 2, 3}$ . The number of relations on $A$ , containing $(2, 3)$ and , which are reflexive and transitive but not symmetric, is .2025 · Numerical
Let $R = {(1, 2), (2, 3), (3, 3)}$ be a relation defined on the set ${1, 2, 3, 4}$ . Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation, is:2025 · MCQ