Read and download free pdf of CBSE Class 12 Mathematics Relations And Functions Assignment Set A. Get printable school Assignments for Class 12 Mathematics. Class 12 students should practise questions and answers given here for Chapter 1 Relations And Functions Mathematics in Class 12 which will help them to strengthen their understanding of all important topics. Students should also download free pdf of Printable Worksheets for Class 12 Mathematics prepared as per the latest books and syllabus issued by NCERT, CBSE, KVS and do problems daily to score better marks in tests and examinations

## Assignment for Class 12 Mathematics Chapter 1 Relations And Functions

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

### Chapter 1 Relations And Functions Class 12 Mathematics Assignment

**Question. Set A has 3 elements and set B has 4 elements. Then the number of injective functions that can be defined from set A to set B is**

(a) 144

(b) 12

(c) 24

(d) 64

**Answer : C**

**Question. Let R be a relation on the set L of lines defined by l1 R l2 if l1 is perpendicular to l2, then relation R is**

(a) reflexive and symmetric

(b) symmetric and transitive

(c) equivalence relation

(d) symmetric

**Answer : D**

**Question. Which of the following functions from Z into Z are bijective?**

(a) f(x) = x^{3}

(b) f(x) = x + 2

(c) f(x) = 2x + 1

(d) f(x) = x^{2} + 1

**Answer : B**

**Question. Let A = R – {3}, B = R – {1}. Let f : A → B be defined by f(x)=(x−2)/(x−3). Then,**

(a) f is bijective

(b) f is one-one but not onto

(c) f is onto but not one-one

(d) None of these

**Answer : A**

**Question. Let f: R → R is defined as f(x) = 3x then f is**

a) f is one-one and onto

b) f is one-one but not onto

c) f is many-one

d) f is neither one-one nor onto

**Answer : A**

**Question. The function f : R → R given by f(x) = x3 – 1 is**

(a) a one-one function

(b) an onto function

(c) a bijection

(d) neither one-one nor onto

**Answer : C**

**Question. Let f : R → R be a function defined by f(x) = x3 + 4, then f is**

(a) injective

(b) surjective

(c) bijective

(d) none of these

**Answer : C**

**Question. Set A has 3 elements and the set B has 4 elements. Then the number of injective functions that can be defined from set A to set B is**

(a) 144

(b) 12

(c) 24

(d) 64

**Answer : C**

**Question. If N be the set of all-natural numbers, consider f : N → N such that f(x) = 2x, ∀ x ∈ N, then f is**

(a) one-one onto

(b) one-one into

(c) many-one onto

(d) None of these

**Answer : B**

**Question. The mapping f : N → N is given by f(n) = 1 + n2, n ∈ N when N is the set of natural numbers is**

(a) one-one and onto

(b) onto but not one-one

(c) one-one but not onto

(d) neither one-one nor onto

**Answer : C**

**Question. The relation R on the set A ={1,2,3} given by R = {(1,1), (1,2), (2,2), (2,3), (3,3)} is**

a) Reflexive

b) Symmetric

c) Transitive

d) Equivalence

**Answer : A**

**Question. Given set A ={1, 2, 3} and a relation R = {(1, 2), (2, 1)}, the relation R will be**

(a) reflexive if (1, 1) is added

(b) symmetric if (2, 3) is added

(c) transitive if (1, 1) is added

(d) symmetric if (3, 2) is added

**Answer : C**

**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 (A) if n (A) = p and n(B) = q The number of relation from set A to B is 𝑝𝑞**

**Reason (R) The number of subset of A X B is 2𝑝𝑞**

**Answer : D**

**Question. Assertion (A) Let A and B be sets. Show that f : A × B →B × A such that f (a, b) = (b, a) is bijective function**

**Reason (R) f is said to equivalence relation if f is reflexive , symmetric and transitive**

**Answer : B**

**Question. Assertion (A)A function f : X →Y is said to be one-one and onto (or bijective)**

**Reason (R) if f is both one-one and onto.**

**Answer : A**

**Question. Assertion (A) Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Then f is one-one.**

**Reason (R) f is bijective function**

**Answer : C**

**Question. Assertion (A) The function f :N→N, given by f (x) = 2x, is not onto
Reason (R) The function f is onto, for f (x) = f (y) ⇒2x = 2y⇒x = y.**

**Answer : C**

**Question. Assertion (A) the function f :N→N, given by f (1) = f (2) = 1 and f (x) = x – 1, for every x > 2, is onto but not one-one.**

**Reason (R) fis not one-one, as f (1) = f (2) = 1. But f is onto, as given any y ∈N, y ≠1, we can choose x as y + 1 such that f (y + 1) = y + 1 – 1 = y. Also for 1 ∈N, we have f (1) = 1.**

**Answer : A**

**Question. Assertion (A) Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function From A to B. Then f is one-one.**

**Reason (R) Since the function f : N→N, given by f (x) = 2x, is not onto**

**Answer : B**

**Question. Assertion (A)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}. R is not equivalence realtion.**

**Reason (R)R is symmetric but neither reflexive nor transitive**

**Answer : A**

**Question. Assertion (A)The relation R in the set Z of integers given by R = {(a, b) : 2 divides a – b} is reflexive and symmetric**

**Reason (R) R is reflexive, as 2 divides (a – a) for all a ∈Z.**

**Answer : B**

**Question. Assertion (A) The number of all one-one functions from set A = {1, 2, 3} to itself is 6**

**Reason (R) if n (A) = p and n(B) = q The number of function from set A to B is 𝑝𝑞**

**Answer : C**

**Case Based Questions**

Raji visited the Exhibition along with her family.

The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = ** **x_{2}.

**Answer the following questions using the above information:**

**Question. Let f: {1, 2, 3,...} → {1, 4, 9, ...} be defined by f(x) = x_{2} is _______ .**

(a) Bijective

(b) Surjective but not injective

(c) Injective but Surjective

(d) Neither Surjective nor Injective

**Answer : A**

**Question. Let f : R → R be defined by f(x) = x_{2} is ____**

(a) Neither Surjective nor Injective

(b) Surjective

(c) Injective

(d) Bijective

**Answer : A**

**Question. Let : N → R be defined by f(x) = x _{2}. Range of the function among the following is ______**

(a) {1, 4, 9, 16, ...}

(b) {1, 4, 8, 9, 10,...}

(c) {1, 4, 9, 15, 16,...}

(d) {1, 4, 8, 16,...}

**Answer : A**

**Question. Let f : N → N be defined by f(x) = x_{2} is _____**

(a) Surjective but not Injective

(b) Surjective

(c) Injective

(d) Bijective

**Answer : C**

**Question. The function f : Z → Z defined by f(x) = x_{2} is ________**

(a) Neither Injective nor Surjective

(b) Injective

(c) Surjective

(d) Bijective

**Answer : A**

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 set of all possible outcomes. A = {S, D}, B = {1, 2, 3, 4, 5, 6}

**Based on the above information answer the following:**

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

(a) 6^{2}

(b) 2^{6}

(c) 6^{!}

(d) 2^{12}

**Answer :D**

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

(a) Reflexive and transitive but not symmetric

(b) Reflexive and symmetric but not transitive

(c) Not reflexive but symmetric and transitive

(d) Equivalence

**Answer : A**

**Question. 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**

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

(a) 6^{2}

(b) 2^{6}

(c) 6^{!}

(d) 2^{12}

**Answer : A**

**Question. 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**

**1 marks question**

**Question. If A= {1, 2, 3} and R is a relation on set A, where R = { (1,1),(2,2), (3,3)} then find R is an equivalence relation or not.**

**Answer :**Yes

**Question. Let A= {1, 2, 3}. Find the number of relation on A containing (1, 2) and (2, 3) which are reflexive and transitive but not symmetric.**

**Answer :**4

**Question. Let A= {1, 2, 3}. Find the number of equivalence relation on A, containing (1, 2) and (2, 1).**

**Answer :**2,

**Question. If f= {(5, 2), (6, 3)}, g= {(2, 5), (3, 6)}, write fog,**

**Answer : {**(2, 2), (3, 3)},

**Question. If A={a, b, c, d}, and f= {(a, b), (b, d), (c, a), (d, c)}, show that f is one-one onto from A to A. Find f**

^{-1}.**Answer :**{(b, a), (d, b), (a, c), (c, d)},

**Question. Consider the set A= {a, b, c}, and R be the smallest equivalence relation on A, then find R.**

**Answer :**{(a, a), (b, b), (c, c)},

**Question. Consider the set A containing n elements. Then the total number of injective functions from A onto itself is--------**

**Answer :**n!

**Question. If f ={(5 ,2), (6 , 3)} and g ={ (2 ,5 ), (3,6) } Find range of f and g.**

**Answer :**{2,3} and {5,6}.

**Please click the below link to access CBSE Class 12 Mathematics Relations And Functions Assignment Set A**

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### CBSE Class 12 Mathematics Chapter 1 Relations And Functions Assignment

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