Domain and Range of a Relation

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JEE Advanced 1979

LEVELJEE Main

Consider the following relations in the set of real numbers $R$ . $R = {(x, y) : x \in R, y \in R, x^{2} + y^{2} \leq 25}$ $R^{'} = {(x, y) : x \in R, y \in R, y \geq \frac{4}{9} x^{2}}$ Find the domain and range of $R \cap R^{'}$ . Is the relation $R \cap R^{'}$ a function?

JEE Main 2018 (16 April Shift 1)

LEVELBoard

Let N denote the set of all natural numbers. Define two binary relations on N as $R_{1} = {(x, y) \in N \times N : 2 x + y = 10}$ and $R_{2} = {(x, y) \in N \times N : x + 2 y = 10}$ . Then :

(A)

Both

R_{1}

and

R_{2}

are symmetric relations

(B)

Range of

R_{1}

{2, 4, 8}

(C)

Both

R_{1}

and

R_{2}

are transitive relations

(D)

Range of

R_{2}

{1, 2, 3, 4}

JEE Main 2020 (2 September Shift 1)

LEVELJEE Main

If $R = {(x, y) : x, y \in Z, x^{2} + 3 y^{2} \leq 8}$ is a relation on the set of integers $Z$ , then the domain of $R^{- 1}$ is:

(A)

{0, 1}

(B)

{- 2, - 1, 1, 2}

(C)

{- 1, 0, 1}

(D)

{- 2, - 1, 0, 1, 2}

JEE Main 2022 (28 June Shift 1)

LEVELBoard

Let $R_{1}$ and $R_{2}$ be relations on the set ${1, 2, \dots, 50}$ such that $R_{1} = {(p, p^{n}) : p is a prime and n \geq 0 is an integer}$ and $R_{2} = {(p, p^{n}) : p is a prime and n = 0 or 1}$ . Then, the number of elements in $R_{1} - R_{2}$ is ________.

JEE Main 2022 (29 July Shift 1)

LEVELBoard

Let $R$ be a relation from the set ${1, 2, 3, \dots, 60}$ to itself such that $R = {(a, b) : b = pq, where p, q \geq 3 are prime numbers}$ . Then, the number of elements in $R$ is :

JEE Main 2023 (06 Apr Shift 1)

LEVELBoard

Let $A = {1, 2, 3, 4, \dots, 10}$ and $B = {0, 1, 2, 3, 4}$ . The number of elements in the relation $R = {(a, b) \in A \times A : 2 (a - b)^{2} + 3 (a - b) \in B}$ is

JEE Main 2023 (15 Apr Shift 1)

LEVELJEE Main

Let $A = {1, 2, 3, 4}$ and $R$ be a relation on the set $A \times A$ defined by $R = {((a, b), (c, d)) : 2 a + 3 b = 4 c + 5 d}$ . Then the number of elements in $R$ is

JEE Main 2026 (22 January Shift 2)

LEVELJEE Main

The number of elements in the relation $R = {(x, y) : 4 x^{2} + y^{2} < 52, x, y \in Z}$ is

JEE Main 2026 (24 January Shift 1)

LEVELJEE Main

Let $R$ be a relation defined on the set ${1, 2, 3, 4} \times {1, 2, 3, 4}$ by $R = {((a, b), (c, d)) : 2 a + 3 b = 3 c + 4 d}$ . Then the number of elements in $R$ is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let N denote the set of all natural numbers. Define two binary relations on N as R1​={(x,y)∈N×N:2x+y=10} and R2​={(x,y)∈N×N:x+2y=10}. Then :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If R={(x,y):x,y∈Z,x2+3y2≤8} is a relation on the set of integers Z, then the domain of R−1 is:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let R be a relation from the set {1,2,3,…,60} to itself such that R={(a,b):b=pq, where p,q≥3 are prime numbers}. Then, the number of elements in R is :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let A={1,2,3,4,…,10} and B={0,1,2,3,4}. The number of elements in the relation R={(a,b)∈A×A:2(a−b)2+3(a−b)∈B} is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let A={1,2,3,4} and R be a relation on the set A×A defined by R={((a,b),(c,d)):2a+3b=4c+5d}. Then the number of elements in R is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The number of elements in the relation R={(x,y):4x2+y2<52,x,y∈Z} is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let R be a relation defined on the set {1,2,3,4}×{1,2,3,4} by R={((a,b),(c,d)):2a+3b=3c+4d}. Then the number of elements in R is

Let N denote the set of all natural numbers. Define two binary relations on N as $R_{1} = {(x, y) \in N \times N : 2 x + y = 10}$ and $R_{2} = {(x, y) \in N \times N : x + 2 y = 10}$ . Then :

If $R = {(x, y) : x, y \in Z, x^{2} + 3 y^{2} \leq 8}$ is a relation on the set of integers $Z$ , then the domain of $R^{- 1}$ is:

Let $R$ be a relation from the set ${1, 2, 3, \dots, 60}$ to itself such that $R = {(a, b) : b = pq, where p, q \geq 3 are prime numbers}$ . Then, the number of elements in $R$ is :

Let $A = {1, 2, 3, 4, \dots, 10}$ and $B = {0, 1, 2, 3, 4}$ . The number of elements in the relation $R = {(a, b) \in A \times A : 2 (a - b)^{2} + 3 (a - b) \in B}$ is

Let $A = {1, 2, 3, 4}$ and $R$ be a relation on the set $A \times A$ defined by $R = {((a, b), (c, d)) : 2 a + 3 b = 4 c + 5 d}$ . Then the number of elements in $R$ is

The number of elements in the relation $R = {(x, y) : 4 x^{2} + y^{2} < 52, x, y \in Z}$ is

Let $R$ be a relation defined on the set ${1, 2, 3, 4} \times {1, 2, 3, 4}$ by $R = {((a, b), (c, d)) : 2 a + 3 b = 3 c + 4 d}$ . Then the number of elements in $R$ is