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Chapter:

relations-and-functions

1. Which of following is not a function?

{(1,2), (2,4), (3,6)} {(-1,1), (-2,4), (2,4)} {(1,2), (1,4), (2,5), (3,8)} {(1,1), (2,2), (3,3)}

{(1,2), (1,4), (2,5), (3,8)}

A relation from a set A to a set B is said to be a function if every element of set A has one and one image in set B.
In {(1,2), (1,4), (2,5), (3,8)}, since element 1 has two images 2 and 4 which is not possible in a function so, it is not a function. Rest all have one and only one image so y can be called a function.

Hint Answer

2. Let A={1,2,3,4,5} and R be a relation from A to A, R = {(x, y): y = x + 1}. Find range.

{1,2,3,4,5} {2,3,4,5} {1,2,3,4} {1,2,3,4,5,6}

{2,3,4,5}

Range is set of elements of codomain which have ir preimage in domain.
Relation R = {(1,2), (2,3), (3,4), (4,5)}.
Range = {2,3,4,5}.

Hint Answer

3. If A X B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)} n find set A.

{1} {1, 2} {1, a} {a, b, c}

{1, 2}

In each ordered pair of A X B, first element belongs to set A and second element belongs to set B.
1,2 ∈ A so, A = {1, 2}.

Hint Answer

4. Find domain of function |x|.

Set of real numbers Set of positive real numbers Set of integers Set of natural numbers

Set of real numbers

Since above function can have all real values of x. So, domain is set of real numbers.

Hint Answer

5. If A={1,4,8,9} and B={1, 2, -1, -2, -3, 3,5} and R is a relation from set A to set B {(x, y): x=y²}. Find domain of relation.

{1,4,9} {-1,1, -2,2, -3,3} {1,4,8,9} {-1,1, -2,2, -3,3,5}

{1,4,8,9}

We know, domain of a relation is set from which relation is defined i.e. set A.
So, domain = {1,4,8,9}.

Hint Answer

6. In a function from set A to set B, image can have more than one preimage.

True False

True

A relation from a set A to a set B is said to be a function if every element of set A has one and one image in set B. A preimage must have one image, an image can have more than one preimage.

Hint Answer

7. Which function is shown in graph?

$Which function is shown in graph?\r\n$

Constant Modulus Identity Signum function

Constant

{(1,5), (2,5), (3,5),……}. This function involves relation {(x, y): y=constant} which is involved in constant function. So, above function is constant function.

Hint Answer

8. Let A={1,2,3,4,5} and R be a relation from A to A, R = {(x, y): y = x + 1}. Find domain.

{1,2,3,4,5} {2,3,4,5} {1,2,3,4} {1,2,3,4,5,6}

{1,2,3,4,5}

We know, domain of a relation is set from which relation is defined i.e. set A.
So, domain = {1,2,3,4,5}.

Hint Answer

9. If P X Q has 10 elements n which is not possible?

n(P)=1 and n(Q)=10 n(P)=10 and n(Q)=1 n(P)=2 and n(Q)=5 n(P)=5 and n(Q)=4

n(P)=5 and n(Q)=4

If set P has m elements and set Q has n elements n P X Q has m*n elements.
m*n=10 => if m=1 n n=10,
if m=2 n n=5,
if m=5 n n=2 and if m=10 n n=1.

Hint Answer

10. If A X B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)} n find set B.

{1} {1, 2} {1, a} {a, b, c}

{a, b, c}

In each ordered pair of A X B, first element belongs to set A and second element belongs to set B.
a, b, c ∈ B so, B = {a, b, c}.

Hint Answer

Nexttt

All Chapters

View all Chapter and number of question available From each chapter from objective-mathematics

Sets

Relations and Functions

Relations and Functions

Trigonometric Functions

Trigonometric Functions

Principle of Mathematical Induction

Principle of Mathematical Induction

Complex Numbers and Quadratic Equations

Complex Numbers and Quadratic Equations

Linear Inequalities

Linear Inequalities

Permutations and Combinations

Permutations and Combinations

Binomial Theorem

Binomial Theorem

Sequences and Series

Sequences and Series

Straight Lines

Conic Sections

Three Dimensional Geometry

Three Dimensional Geometry

Limits and Derivatives

Limits and Derivatives

Mathematical Reasoning

Mathematical Reasoning

Statistics

Probability

Relations and Functions II

Relations and Functions

Inverse Trigonometric Functions

Inverse Trigonometric Functions

Matrices

Determinants

Continuity and Differentiability

Continuity and Differentiability

Application of Derivatives

Application of Derivatives

Integrals

Application of Integrals

Application of Integrals

Differential Equations

Differential Equations

Vector Algebra

Three Dimensional Geometry

Three Dimensional Geometry

Linear Programming

Linear Programming

Probability

Application of Calculus

Application of Calculus

Topics

This Chapter relations-and-functions consists of the following topics

Relations and Functions

Which of following is not a function?

Let A={1,2,3,4,5} and R be a relation from A to A, R = {(x, y): y = x + 1}. Find range.

If A X B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)} n find set A.

Find domain of function |x|.

If A={1,4,8,9} and B={1, 2, -1, -2, -3, 3,5} and R is a relation from set A to set B {(x, y): x=y²}. Find domain of relation.

In a function from set A to set B, image can have more than one preimage.

Which function is shown in graph?

$Which function is shown in graph?\r\n$

;

Let A={1,2,3,4,5} and R be a relation from A to A, R = {(x, y): y = x + 1}. Find domain.

If P X Q has 10 elements n which is not possible?

If A X B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)} n find set B.

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