A relation R is defined in the set Z of integers as follows x , y ∈ R if and only if x 2 + y 2 = 9 . Which of the following is false?

R = 0 , 3 , 0 , − 3 , 3 , 0 , − 3 , 0

If A = x / x ≤ 10 , x ∈ N and B = x / x ≤ 10 , x ∈ W , then A ∩ B = ?

1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10

If A = { 2 , 4 } , B = { 3 , 4 , 5 } , then ( A ∩ B ) × ( A ∪ B ) =

{ ( 4 , 2 ) , ( 4 , 3 ) , ( 4 , 4 ) , ( 4 , 5 ) }

{ ( 3 , 2 ) , ( 3 , 4 ) , ( 4 , 4 ) , ( 5 , 4 ) }

{ ( 4 , 3 ) , ( 4 , 4 ) , ( 4 , 5 ) }

{ ( 2 , 3 ) , ( 2 , 4 ) , ( 2 , 5 ) }

Let N denote the set of all natural numbers. Define two binary relations on N as R 1 = x , y ∈ N × N : 2 x + y = 10 and R 2 = x , y ∈ N × N : x + 2 y = 10 . Then

both R 1 and R 2 are transitive relations

both R 1 and R 2 are symmetric relations

EASY

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The function $f (x) = 2^{x}$ is

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Important Questions on Relations and Functions

EASY

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

Let

R

be the relation in the set

N

given by

R = {(a, b) : a = b - 2, b > 6}

. Then

EASY

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

If set

A = {x : x is a measure of an angle of scalen triangle}

, then the number of relation containing (measure of minimum angle, measure of maximum angle) is

EASY

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

A relation

R

is defined in the set

Z

of integers as follows

(x, y) \in R

if and only if

x^{2} + y^{2} = 9

. Which of the following is false?

EASY

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

Let

A = \{2, 3, 4\}

and

B = \{8, 9, 12\}

. Then the number of elements in the relation

R = \{((a_{1}, b_{1}), (a_{2}, b_{2})) \in (A \times B, A \times B) : a_{1} divides b_{2} and a_{2} divides b_{1}\}

EASY

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

Consider the following relations in the real numbers

R_{1} = \{(x, y) ∣ x^{2} + y^{2} \leq 25\}

and

R_{2} = \{(x, y), y \geq \frac{4 x^{2}}{9}\}

, then the range of

R_{1} \cap R_{2}

EASY

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

Let

A = \{1, 2, 3, 4, 5\}

and let

B = \{1, 2, 3, 4\}

. If the relation

R : A \to B

is given by

(a, b) \in R

if and only if

a + b

is even, then

n (R)

is equal to

EASY

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

Let $R$ be the relation on the set $N$ given by $R = {(a, b) : a = b - 2, b > 6}$ . Choose the correct answer.

EASY

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

If $A = \{x / x \leq 10, x \in N\}$ and $B = \{x / x \leq 10, x \in W\}$ , then $A \cap B = ?$

MEDIUM

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

Let

A

be a set consisting of

10

elements. The number of non-empty relations from

A

A

that are reflexive but not symmetric is

EASY

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

Let

A, B, C

are three non-empty sets. The number of relations from

A

B

64

, that of

B

C

4096

and that of

A

C

256

. Then the numbers of elements of the sets are in

HARD

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

In an examination

51 %

students fail in English and

45 %

fail in Maths. If

21 %

students fail in both the subjects, then

169

students pass the examination. What is the total number of students taking the exam?

EASY

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

Let

A = {2, 3, 4, 5}, B = {36, 45, 49, 60, 77, 90}

and let

R

be the relation 'is factor of' from

A

B

. Then the range of

R

is the set

MEDIUM

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

In a group of boys,

25

play volleyball,

20

play badminton and

10

boys play cricket. Five boys play all the three games. 8 boys play atleast two of the three games. How many of them play only one game?

EASY

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

Let

R

be a relation in the set

N

of natural numbers given by

R = {(a, b) : a = b - 2}

. Choose the correct answer.

MEDIUM

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

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}

HARD

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

The number of ordered pairs

(a, b)

of positive integers such that

\frac{2 a - 1}{b}

and

\frac{2 b - 1}{a}

are both integers is

EASY

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

A = {2, 4}, B = {3, 4, 5},

then

(A \cap B) \times (A \cup B) =

EASY

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

If there are

2

elements in a set

A,

then what would be the number of possible relations from the set

A

to set

A ?

MEDIUM

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

n (A) = 2

and total number of possible relations from set

A

to set

B

1024

, then

n (B)

EASY

Mathematics>Algebra>Relations and Functions>Domain and Range of the Relation

Let

N

denote the set of all natural numbers. Define two binary relations on

N

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

The function f(x)=2x is

Important Questions on Relations and Functions

Learn and Prepare for any exam you want !

The function $f (x) = 2^{x}$ is