Read and download free pdf of CBSE Class 12 Mathematics Relations And Functions Worksheet Set F. Students and teachers of Class 12 Mathematics can get free printable Worksheets for Class 12 Mathematics Chapter 1 Relations and Functions in PDF format prepared as per the latest syllabus and examination pattern in your schools. Class 12 students should practice questions and answers given here for Mathematics in Class 12 which will help them to improve your knowledge of all important chapters and its topics. Students should also download free pdf of Class 12 Mathematics Worksheets prepared by school teachers as per the latest NCERT, CBSE, KVS books and syllabus issued this academic year and solve important problems with solutions on daily basis to get more score in school exams and tests

## Worksheet for Class 12 Mathematics Chapter 1 Relations and Functions

Class 12 Mathematics students should refer to the following printable worksheet in Pdf for Chapter 1 Relations and Functions in Class 12. This test paper with questions and answers for Class 12 will be very useful for exams and help you to score good marks

### Class 12 Mathematics Worksheet for Chapter 1 Relations and Functions

CBSE Class 12 Mathematics Worksheet - Relations And Functions. CBSE issues sample papers every year for students for class 12 board exams. Students should solve the CBSE issued sample papers to understand the pattern of the question paper which will come in class 12 board exams this year. The sample papers have been provided with marking scheme. It’s always recommended to practice as many CBSE sample papers as possible before the board examinations. Sample papers should be always practiced in examination condition at home or school and the student should show the answers to teachers for checking or compare with the answers provided. Students can download the sample papers in pdf format free and score better marks in examinations. Refer to other links too for latest sample papers.

**Question. Let f: 𝑅 → 𝑅 be defined as f(x) =3x - 2. Choose the correct answer.**

a) f is one-one onto

b) f is many one onto

c) f is one-one but not onto

d) f is neither one-one nor onto**Answer : A**

**Question. Let us define a relation R in R as aRb if a ≥ b. Then R is**

(a) an equivalence relation

(b) reflexive, transitive but not symmetric

(c) symmetric, transitive but not reflexive

(d) neither transitive nor reflexive but symmetric**Answer : B**

**Question. let R be the relation in the set N given by R={(a,b):a=b-2,b>6}.Choose the correct answer.**

(a) (2,4)€R

(b) (3,8) € R

(c) (6,8)€ R

(d) (8,10) € R**Answer : D**

**Question. Let R be a relation on set of lines as L1 R L2 if L1 is perpendicular to L2. Then**

a) R is Reflexive

b) R is transitive

c) R is symmetric

d) R is an equivalence relation**Answer : C**

**Question. Let R be a relation on the set N of natural numbers denoted by nRm⇔ n is a factor of m (i.e. n | m). Then, R is**

(a) Reflexive and symmetric

(b) Transitive and symmetric

(c) Equivalence

(d) Reflexive, transitive but not symmetric**Answer : D**

**Question. A Relation from A to B is an arbitrary subset of:**

a) AxB

b) BxB

c) AxA

d) BxB**Answer : A**

**Question. Let R be a relation defined on Z as R= {(a,b) ; a2+b2=25 } , the domain of R is;**

(a) {3,4,5}

(b) {0,3,4,5}

(c) {0,3,4,5,-3,-4,-5}

(d) none**Answer : C**

**Question. Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b ∀ a, b ∈ T. Then R is**

(a) reflexive but not transitive

(b) transitive but not symmetric

(c) equivalence

(d) None of these**Answer : C**

**Question. The maximum number of equivalence relations on the set A = {1, 2, 3} are**

(a) 1

(b) 2

(c) 3

(d) 5**Answer : D**

**Question. Let S = {1, 2, 3, 4, 5} and let A = S × S. Define the relation R on A as follows: (a, b) R (c, d) iff ad = cb. Then, R is**

(a) reflexive only

(b) Symmetric only

(c) Transitive only

(d) Equivalence relation**Answer : D**

**Question. Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is**

(a) reflexive but not symmetric

(b) reflexive but not transitive

(c) symmetric and transitive

(d) neither symmetric, nor transitive**Answer : A**

**Question. Let A = {x : -1 ≤ x ≤ 1} and f : A → A is a function defined by f(x) = x |x| then f is**

(a) a bijection

(b) injection but not surjection

(c) surjection but not injection

(d) neither injection nor surjection**Answer : A**

**Question. Let X = {-1, 0, 1}, Y = {0, 2} and a function f : X → Y defined by y = 2x4, is**

(a) one-one onto

(b) one-one into

(c) many-one onto

(d) many-one into**Answer : C**

**Question. Let f : [0, ∞) → [0, 2] be defined by f(x) = 2x/1 + x, then f is**

(a) one-one but not onto

(b) onto but not one-one

(c) both one-one and onto

(d) neither one-one nor onto**Answer : B**

**Question. Given set A = {a, b, c). An identity relation in set A is **

(a) R = {(a, b), (a, c)}

(b) R = {(a, a), (b, b), (c, c)}

(c) R = {(a, a), (b, b), (c, c), (a, c)}

(d) R= {(c, a), (b, a), (a, a)}**Answer : B**

**CASE STUDY**

A relation R on a set A is said to be an equivalence relation on A if it is

• Reflexive i.e., (a, a) ∈ R ∀ a ∈ A.

• Symmetric i.e., (a, b) ∈ R ⇒ (b, a) ∈ R ∀ a, b ∈ A.

• Transitive i.e., (a, b) ∈ R and (b, c) ∈ R ⇒ (a, c) ∈ R ∀ a, b, c ∈A. Based on the above information, answer the following questions:

**Question. If the relation R = {(1, 1), (1, 2), (1, 3), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)} defined on the set A = {1, 2, 3}, then R is**

(a) reflexive

(b) symmetric

(c) transitive

(d) equivalence**Answer : A**

**Question. If the relation R = {(1, 2), (2, 1), (1, 3), (3, 1)} defined on the set A = {1, 2, 3}, then R is**

(a) reflexive

(b) symmetric

(c) transitive

(d) equivalence**Answer : B**

**Question. If the relation R on the set N of all natural numbers defined as R = {(x, y) : y = x + 5 and (x <4), then R is**

(a) reflexive

(b) symmetric

(c) transitive

(d) equivalence**Answer : C**

**CASE STUDY**

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes.A = {S, D}, B = {1,2,3,4,5,6}

**1. Let 𝑅∶ 𝐵→𝐵 be defined by R = {(𝑥,): 𝑦 𝑖𝑠 𝑑𝑖𝑣𝑖𝑠𝑖𝑏𝑙𝑒 𝑏 } is**

a. Reflexive and transitive but not symmetric

b. Reflexive and symmetric and not transitive

c. Not reflexive but symmetric and transitive

d. Equivalence**Answer : A**

**2. Raji wants to know the number of functions from A to B. How many number of functions are possible?**

a. 62

b. 26

c. 6!

d. 212**Answer : A**

**3. Let R be a relation on B defined by R = {(1,2), (2,2), (1,3), (3,4), (3,1), (4,3), (5,5)}. Then R is**

a. Symmetric

b. Reflexive

c. Transitive

d. None of these three**Answer : D**

**4. Raji wants to know the number of relations possible from A to B. How many numbers of relations are possible?**

a. 62

b. 26

c. 6!

d. 212**Answer : D**

**5. Let 𝑅:𝐵→𝐵 be defined by R={(1,1),(1,2), (2,2), (3,3), (4,4), (5,5),(6,6)}, then R is**

a. Symmetric

b. Reflexive and Transitive

c. Transitive and symmetric

d. Equivalence**Answer : B**

**ASSERTION AND REASON**

**Read Assertion and reason carefully and write correct option for each question**

(a) Both A and R are correct; R is the correct explanation of A.

(b) Both A and R are correct; R is not the correct explanation of A.

(c) A is correct; R is incorrect.

(d) R is correct; A is incorrect.

**Question. Assertion= {(T1, T2) : T1 is congruent to T2}. Then R is an equivalence relation.****Reason(R) Any relation R is an equivalence relation, if it is reflexive, symmetric and transitive****Answer : A**

**Question. Assertion (A) Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y) :x and y have same number of pages} is not equivalence relation.****Reason (R) Since R is reflexive, symmetric and transitive.****Answer : C**

**Question. Assertion (A) Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. R is an equivalence relation****Reason (R) Since R is reflexive, symmetric but R is not transitive.****Answer : C**

**Question. Assertion (A) A one-one function f : {1, 2, 3} →{1, 2, 3} must be onto.****Reason (R) Since f is one-one, three elements of {1, 2, 3} must be taken to 3 different elements of the co- domain {1, 2, 3} under f.****Answer : A**

**Question. Assertion (A) The relation R in R defined as R = {(a, b) :a≤𝑏2} is not equivalence relation.****Reason (R) Since R is not reflexive but it is symmetric and transitive.****Answer : A**

**Question. Assertion (A)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. Reason (R) R is not symmetric, as (1, 2) ∈R but (2, 1) ∉R. Similarly, R is not transitive, as (1, 2) ∈R and (2, 3) ∈R but (1, 3) ∉ R.**

**Answer : A**

**Question. Assertion (A) The Modulus Function f :R→R, given by f (x) = | x | is not one one and onto function****Reason (R) The Modulus Function f :R→R, given by f (x) = | x | is bijective function****Answer : C**

**Question. Assertion (A) The function f :N→N, given by f (x) = 2x, is one-oneReason (R) The function f is one-one, for f (x) = f (y) ⇒2x = 2y⇒x = y.**

**Answer : A**

**Question. Assertion (A) Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4,4), (1, 3), (3, 3), (3, 2)}. R is not equivalence relation.****Reason (R) R is not Reflexive relation but it is symmetric and transitive****Answer : C**

**Question. Assertion (A) The relation R in R defined as R = {(a, b) :a≤b} is not equivalence relation.****Reason (R) Since R is not reflexive but it is symmetric and transitive.****Answer : C**

Q1 Let n be a fixed positive integer. Define a relation R on Z as follows (a, b) Є R a-b is divisible by n. Show that R is an equivalence relation on z.

Q2. Let z be the set of integers show that the relation R = [a, b) : a, b Є z and a + b is even] is an equivalence relation on z.

Q3. Let S be a relation on the set R of real numbers defined by S = [(a, b) Є R x R : a^{2} + b^{2} = 1} prove that S is not an equivalence relation R.

Q4. Show that the relation R on the set R of real numbers defined as R = [(a, b) : : a < b^{2}] is neither reflexive nor symmetric nor transitive.

Q5. Show that the relation R on R defined as R = [(a, b) : a < ] is reflexive and transitive but not symmetric.

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### CBSE Class 12 Mathematics Chapter 1 Relations and Functions Worksheet

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