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NCERT Solutions for Class 12 Mathematics Mathematics Part I Chapter 1 Relations And Functions

Relations And Functions Here is the CBSE Mathematics Chapter 1 for Class 12 students. Summary and detailed explanation of the lesson, including the definitions of difficult words. All of the exercises and questions and answers from the lesson's back end have been completed. NCERT Solutions for Class 12 Mathematics Relations And Functions Chapter 1 NCERT Solutions for Class 12 Mathematics Relations And Functions Chapter 1 The following is a summary in Hindi and English for the academic year 2025-26. You can save these solutions to your computer or use the Class 12 Mathematics.

Question 1

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Consider the following information regarding the number of men and women workers in three factories I. II and III

Men Workers

Women Workers

I

30

25

II

25

31

III

27

26

Represent the above information in the form of a 3 x 2 matrix. What does the entry in the third row and second column represent?

Solution

The given information is

Factory	Men Workers	Women Worker:
I	, 30	25
II	' 25	31
III	27	26

The information is represented in the form of a 3 X 2 matrix as follows :
$A equals open square brackets table row 30 25 row 25 31 row 27 26 end table close square brackets$
The entry in the third row and second column represents the number of women workers in factory III.
$straight A equals open square brackets table row 2 row 35 row cell square root of 3 end cell end table space table row 5 row cell negative 2 end cell row 1 end table table row 19 row cell 5 over 2 end cell row cell negative 5 end cell end table table row cell negative 7 end cell row 12 row 17 end table close square brackets. space write$

Question 2

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If a matrix has 24 elements, what are the possible orders it can have ? Wh'at. if it has 13 elements ?

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Question 3

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lf a matrix has 18 elements, what are the possible orders it can have ? What, if it has 5 elements?

Easy

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Question 4

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If a matrix A has 12 elements, what arc the possible orders it can have 7 What if it has 7 elements ?

Easy

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Question 5

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Construct a 3 x 3 matrix w'hose elements are giv en by a,1, = 2 i – 3 j

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Question 6

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Let A be the set of all students of a boys school. Show that the relation R in A given by R = {(a, b) : a is sister of b} is the empty relation and R’ = {(a, b) : the difference between heights of a and b is less than 3 meters} is the universal relation.

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Question 7

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Show that the relation R in the set {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} is reflexive but neither symmetric nor transitive.

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Question 8

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Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

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Question 9

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Give an example of a relation which is

(i) Symmetric but neither reflexive nor transitive.
(ii) Transitive but neither reflexive nor symmetric.
(iii) Reflexive and symmetric but not transitive.
(iv) Reflexive and transitive but not symmetric.
(v) Symmetric and transitive but not reflexive.

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Question 10

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Let L be the set of all lines in a plane and R be the relation in L defined as R = {(L₁, L₂) : L₁ is perpendicular to L₂}. Show that R is symmetric but neither reflexive nor transitive.

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NCERT Solutions for Class 12 Mathematics Mathematics Part I Chapter 1 Relations And Functions

If a matrix has 24 elements, what are the possible orders it can have ? Wh'at. if it has 13 elements ?

lf a matrix has 18 elements, what are the possible orders it can have ? What, if it has 5 elements?

If a matrix A has 12 elements, what arc the possible orders it can have 7 What if it has 7 elements ?

Construct a 3 x 3 matrix w'hose elements are giv en by a,1, = 2 i – 3 j

Let A be the set of all students of a boys school. Show that the relation R in A given by R = {(a, b) : a is sister of b} is the empty relation and R’ = {(a, b) : the difference between heights of a and b is less than 3 meters} is the universal relation.

Show that the relation R in the set {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} is reflexive but neither symmetric nor transitive.

Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

Give an example of a relation which is

(i) Symmetric but neither reflexive nor transitive.
(ii) Transitive but neither reflexive nor symmetric.
(iii) Reflexive and symmetric but not transitive.
(iv) Reflexive and transitive but not symmetric.
(v) Symmetric and transitive but not reflexive.

Let L be the set of all lines in a plane and R be the relation in L defined as R = {(L₁, L₂) : L₁ is perpendicular to L₂}. Show that R is symmetric but neither reflexive nor transitive.

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NCERT Sample Papers

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NCERT Solutions for Class 12 Mathematics Mathematics Part I Chapter 1 Relations And Functions

Consider the following information regarding the number of men and women workers in three factories I. II and III Men Workers Women Workers I 30 25 II 25 31 III 27 26 Represent the above information in the form of a 3 x 2 matrix. What does the entry in the third row and second column represent?

If a matrix has 24 elements, what are the possible orders it can have ? Wh'at. if it has 13 elements ?

lf a matrix has 18 elements, what are the possible orders it can have ? What, if it has 5 elements?

If a matrix A has 12 elements, what arc the possible orders it can have 7 What if it has 7 elements ?

Construct a 3 x 3 matrix w'hose elements are giv en by a,1, = 2 i – 3 j

Let A be the set of all students of a boys school. Show that the relation R in A given by R = {(a, b) : a is sister of b} is the empty relation and R’ = {(a, b) : the difference between heights of a and b is less than 3 meters} is the universal relation.

Show that the relation R in the set {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} is reflexive but neither symmetric nor transitive.

Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

Give an example of a relation which is (i) Symmetric but neither reflexive nor transitive.(ii) Transitive but neither reflexive nor symmetric.(iii) Reflexive and symmetric but not transitive.(iv) Reflexive and transitive but not symmetric.(v) Symmetric and transitive but not reflexive.

Let L be the set of all lines in a plane and R be the relation in L defined as R = {(L1, L2) : L1 is perpendicular to L2}. Show that R is symmetric but neither reflexive nor transitive.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Give an example of a relation which is

(i) Symmetric but neither reflexive nor transitive.
(ii) Transitive but neither reflexive nor symmetric.
(iii) Reflexive and symmetric but not transitive.
(iv) Reflexive and transitive but not symmetric.
(v) Symmetric and transitive but not reflexive.

Let L be the set of all lines in a plane and R be the relation in L defined as R = {(L₁, L₂) : L₁ is perpendicular to L₂}. Show that R is symmetric but neither reflexive nor transitive.