# MCQs For NCERT Class 12 Mathematics Chapter 1 Relations and Functions

Please refer to the MCQ Questions for Class 12 Mathematics Chapter 1 Relations and Functions with Answers. The following Relations and Functions Class 12 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 12. Our experts have designed MCQ Questions for Class 12 Mathematics with Answers for all chapters in your NCERT Class 12 Mathematics book.

## Relations and Functions Class 12 MCQ Questions with Answers

See below Relations and Functions Class 12 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

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) and (2,2) are added
(d) Symmetric if (3, 2) is added

C

Question: Consider the following relations R= {(x,y ) |x and yare real numbers and x= wy for some rational number w}; S=

m, n, p and q  are integers such that n, q ≠ 0 and qm = pn}.Then,
(a) R is an equivalence relation but S is not an equivalence relation.
(b) neither R nor S is an equivalence relation.
(c) S is an equivalence relation but R is not an equivalence relation.
(d) R and S both are equivalence relations.

C

Question: If A = sin2x + cos2 x, then for all real x
(a) 13/16≤ A ≤1
(b) 1 ≤ A ≤ 2
(c) 3/4 ≤A ≤
(d) 3/4 ≤A ≤ 1

D

Question: For real x, let f (x) = x3+5x+1,  then
(a) f is one one but not onto R
(b) f is onto R but not oneone
(c) f is oneone and onto R
(d) f is neither one one nor onto R

C

Question:

D

Question: Let W denotes the words in the English dictionary.
Define the relation R by R= {(x ,y )∈ W x W: the words x and y have at least one letter in common}.Then, R is
(a) reflexive, symmetric but not transitive
(b) reflexive, symmetric and transitive
(c) reflexive, not symmetric and transitive
(d) not reflexive, symmetric and transitive

A

Question: Let R be the real line. Consider the following subsets of the plane Rx R.

and
Which one of the following is true?
(a) T is an equivalence relation on R but S is not.
(b) Neither S nor T is an equivalence relation on R.
(c) Both S and T are equivalence relations on R.
(d) S is an equivalence relation on R but T is not.

A

Question: Let R = {(3,3) ,(6,6), (9,9), (12,12), (6,12), (3,9 ), (3,12)}, (3,6)} a relation on the set A = {3,6,9,12}.The relation is
(a) an equivalence relation
(b) reflexive and symmetric
(c) reflexive and transitive
(d) only reflexive

C

Question. Set A has 4 elements and the set B has 5 elements. Then the number of injective mappings that can be defined from A to B is
(a) 144
(b) 12
(c) 120
(d) 64

C

Question. Given set A = {p, q, r}. An identity relation in set A is
(a) R = {(p, q), (p, r)}
(b) R = {(p, p), (q, q), (r, r)}
(c) R = {(p, p), (q, q), (r, r), (p, r)}
(d) R = {(r, p), (q, p), (p, p)}

B

Question. Let L denote the set of all straight lines in a plane. Let a relation R be defined by 𝑙 R m if and only if 𝑙is perpendicular to m for all 𝑙, m ∈ L. Then R is
(a) Reflexive
(b) Symmetric
(c) Transitive
(d) none of these

B

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

D

Question. Consider the non-empty set consisting of children in a family and a relation R defined as pRq if p is sister of q. Then R is
(a) Symmetric but not Transitive
(b) Transitive but not Symmetric
(c) Neither Symmetric nor Transitive
(d) both Symmetric and Transitive

D

Question. Given triangles with sides T1 ( 3, 4, 5) T2 (5, 12, 13) T3 ( 6, 8, 10) T4 ( 4, 7, 9) and a relation R in set of triangles defined as R = {(T1,T2) : T1 is similar to T2}. Which triangles belong to the same equivalence class?
(a) T1 and T2
(b) T2 and T3
(c) T1 and T3
(d) T1 and T4.

C

Question. A relation S in the set of real numbers is defined as xSy⇒ x – y + √11 is an irrational number, then relation S is
(a) Reflexive
(b) Reflexive and symmetric
(c) Transitive
(d) Equivalence.

D

Question. Let R be a relation on the set N of natural numbers defined by yRx if y divides x. Then R is
(a) Reflexive and symmetric
(b) Transitive and symmetric
(c) Equivalence
(d) Reflexive, transitive but not symmetric

D

Question. Let N be the set of natural numbers and the function f : N → N be defined by f (n) = 5n + 7∀n ∈N. Then f is:
(a) Surjective
(b) Injective
(c) Bijective
(d) None of these

B

Question. If f : R → R be defined by f (x) = 1/x, ∀ x ∈ R. Then, f is
(a) one-one
(b) onto
(c) bijective
(d) f is not defined

D

Question. If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is
(a) reflexive
(b) transitive
(c) symmetric
(d) None of these

B

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

C

Question. If f : R → R be defined by f (x) = 3x2 – 5 and g : R → R by

A

Question. Which of the following functions from Z into Z are bijections?
(a) f(x) = x3
(b) f(x) = x + 2
(c) f(x) = 2x + 1
(d) f(x) = x2 + 1

B

Question. If 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

A

Question. The identity element for the binary operation * defined on Q – {0} as a * b = ab/2 = a, b, ∈ 0 – {0} is
(a) 1
(b) 0
(c) 2
(d) None of these

C

Question. The maximum number of equivalence relations on the set A = {1, 2, 3} are
(a) 1
(b) 2
(c) 3
(d) 5

D

Question. If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is
(a) 720
(b) 120
(c) 0
(d) None of these

C

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

B

Question. If f : R → R be the functions defined by f (x) = x3 + 5, then f -1(x) is
(a) (x + 5)1/3
(b) (x – 5)1/3
(c) (5 – x )1/3
(d) 5 – x

A

Question. If f : A → B and g : B → C be the bijective functions, then (gof )-1 is
(a) f-1 og-1
(b) fog
(c) g-1 of-1
(d) gof

A

Question.

A

Question. If A = {1, 2, 3,,,,,,,,,n} and B = {a, b}. Then, the number of surjections from A into B is
(a) nP2
(b) 2n – 2
(c) 2n – 1
(d) None of these

D

Question. Consider the non-empty set consisting of children in a family and a relation R defined as aRb, if a is brother of b. Then, R is
(a) symmetric but not transitive
(b) transitive but not symmetric
(c) neither symmetric nor transitive
(d) both symmetric and transitive

B

Question.

(a) constant
(b)1+ x
(c) x
(d) None of these

C

Question. If f : [2, ∞) → R be the function defined by f (x) = x2 – 4x + 5, then the range of f is
(a) R
(b) [1, ∞)
(c) [4, ∞)
(d) [5, ∞)

B

Question.

(a) 1
(b) 1
(c) 7/2
(d) None of these

D

Question.

(a) 9
(b) 14
(c) 5
(d) None of these

A

Question. If f : R → R be given by f (x) = tan x, then f -1 (1) is

A

True/False

Question. Every relation which is symmetric and transitive is also reflexive.

False

Question. An integer m is said to be related to another integer n, if mis a integral multiple of n. This relation in Z is reflexive, symmetric and transitive.

False

Question. The composition of function is associative.

True

Question. Every function is invertible.

False

Question. Let R ={(3, 1), (1, 3), (3, 3)} be a relation defined on the set
A ={1, 2, 3}. Then, R is symmetric, transitive but not reflexive.

False

Question. If f : R → R be the function defined by f (x) = sin(3x + 2)∀ x ∈ R.
Then, f is invertible.

False

Question. If A = {0, 1} and N be the set of natural numbers. Then, the mapping f : N → A defined by f (2n – 1) = 0, f (2n) = 1, ∀ n ∈ N, is onto.

True

Question. A binary operation on a set has always the identity element.

False

Question. The relation R on the set A ={1, 2, 3} defined as R ={(1, 1), (1, 2), (2, 1), (3, 3)} is reflexive, symmetric and transitive.

False

Question. The composition of function is commutative.

False

Assertion Reasoning Based Questions :

Question. Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
(A) Both the A and the R are true and R is the correct explanation of A
(B) Both A and R are true but R is not the correct explanation of A
(C) A is true but R is false.
(D) A is false but R is true.
(E) Both A and R is false
Assertion: For two sets A=R-{3} and B=R-{1} defined a function f: A→B as f(x) = x – 2/x – 3 is bijective .
Reason : A function f:A→B is said to be surjective if for all y∈B,∃, x∈ 𝐴 such that f(x)=y

B

Question. Directions: In the following questions, the Assertion (A) and Reason( (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
(A) Both the A and the R are true and R is the correct explanation of A
(B) Both A and R are true but R is not the correct explanation of A
(C) A is true but R is false.
(D) A is false but R is true.
(E) Both A and R are false.
Assertion: A relation R={(a,b) : |a-b| < 2} defined on set A={1,2,3,4,5} is reflexive.
Reason : A relation R on set A is said to be reflexive for (a, b) ∈ 𝑅 and (b, c) ∈ 𝑅 We have (a, c) ∈ 𝑅

C

Question. Directions: In the following questions, the Assertion (A) and Reason ( (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
(A) Both the A and the R are true and R is the correct explanation of A
(B) Both A and R are true but R is not the correct explanation of A
(C) A is true but R is false.
(D) A is false but R is true.
(E) Both A and R are false
Assertion: The Greatest integer Function 𝑓: 𝑅 → 𝑅 is given by 𝑓(𝑥) = [𝑥] is not onto
Reason : A function 𝑓: 𝐴 → 𝐵 is said to be injective if 𝑓(𝑎) = 𝑓(𝑏) ⟹ 𝑎 = 𝑏

B

Question. Directions: In the following questions, the Assertion (A) and Reason ( (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
(A) Both the A and the R are true and R is the correct explanation of A
(B) Both A and R are true but R is not the correct explanation of A
(C) A is true but R is false.
(D) A is false but R is true.
(E) Both A and R are false.
Assertion: Domain and range of the relation R={(𝑥, 𝑦): 𝑥 − 2𝑦 = 0} defined on the set A={1,2,3,4} are respectively {1,2,3,4} and {2,4,6,8}
Reason : Domain and Range of a relation R are respectively the sets {a: a∈A and (a, b)∈ 𝑅} and {b: b ∈A and (a, b)∈ 𝑅}

D

Question. Directions: In the following questions, the Assertion (A) and Reason (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
(A) Both the A and the R are true and R is the correct explanation of A
(B) Both A and R are true but R is not the correct explanation of A
(C) A is true but R is false.
(D) A is false but R is true.
(E) Both A and R are false
Assertion: the relation R in the set A ={ 1,2,3,4,5,6} defined as R={(x, y) : y is divisible by x } is an equivalence relation
Reason :A relation R on the set A is equivalence if it is Reflexive, symmetric and transitive .

D

Question. Directions: In the following questions, the Assertion (A) and Reason ( (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
(A) Both the A and the R are true and R is the correct explanation of A
(B) Both A and R are true but R is not the correct explanation of A
(C) A is true but R is false.
(D) A is false but R is true.
(E) Both A and R are false.
Assertion: A relation R={(1,1), (1,2), (2,2), (2,3), (3,3)} is defined on the set A ={1,2,3} is symmetric
Reason : A relation R on set A is said to be symmetric if (a, b)∈ 𝑅, then (b, a)∈ 𝑅

D

Question. Directions: In the following questions, the Assertion (A) and Reason (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
(A) Both the A and the R are true and R is the correct explanation of A
(B) Both A and R are true but R is not the correct explanation of A
(C) A is true but R is false.
(D) A is false but R is true.
(E) Both A and R are false
Assertion: The Function 𝑓: 𝑍 → 𝑍 is given by 𝑓(𝑥) = 𝑥2 is injective
Reason : A function 𝑓: 𝐴 → 𝐵 is said to be injective if every element of B has a pre image in A

E

Case Based Questions :

In Sh. Sksharma memorial match under 2 different categories-boys and girls. Totally there were 250 participants. Among all of them finally three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project Let B = {𝑏1, 𝑏2, 𝑏3} G= {𝑔1, 𝑔2} where B represents the set of boys selected and G the set of girls who were selected for the final race.

Avi decides to explore these sets for various types of relations and functions

Question. Ravi wants to know among those relations, how many functions can be formed from B to G?
(a) 22
(b) 212
(c) 32
(d) 23

C

Question. Let 𝑅: 𝐵 → 𝐺 be defined by R = {(𝑏1, 𝑔1), (𝑏2, 𝑔2), (𝑏3, 𝑔3)}, then R is__________
(a) Injective
(b) Surjective
(c) Neither Surjective nor Injective
(d) Surjective and Injective

B

Question. Avi wants to find the number of injective functions from B to G. How many numbers of injective functions are possible?
(a) 0
(b) 2!
(c) 3!
(d) 0!

A

Question. Avi wishes to form all the relations possible from B to G. How many such relations are possible?
(a) 26
(b) 25
(c) 0
(d) 23

A

Question. Let R: B→B be defined by R = {(𝑥, 𝑦): 𝑥 and y are students of same sex}, Then this relation R is_______
(a) Equivalence
(b) Reflexive only
(c) Reflexive and symmetric but not transitive
(d) Reflexive and transitive but not symmetric

B

There are two small libraries A and B Both the libraries have four books each . library A has different books for science students whereas library B has different books for non-science students.

No of pages of each book of both the libraries is given in the table given below –

Library A

Library B

Let 𝑅1 = {(𝑀𝑎𝑡ℎ𝑠 , 𝑃ℎ𝑦𝑠𝑖𝑐𝑠), (𝐶ℎ𝑒𝑚𝑖𝑠𝑡𝑟𝑦, 𝐵𝑖𝑜𝑙𝑜𝑔𝑦)} be a relation on A and 𝑅2={(Economics ,Accountancy),( Economics ,History), (Accountancy, History) be a relation B
On the basis of the information given above the information, answer the following:

Question. The relation 𝑅1 on A is
(a) Reflexive only
(b) Symmetric only
(c) Reflexive and transitive
(d) Transitive only

D

Question. The relation 𝑅1 on A is
(a) Reflexive only
(b) Symmetric only
(c) Reflexive and symmetric but not transitive
(d) Transitive but not symmetric

D

Question. Let { ( Maths ,Maths), ( physics, physics) (chemistry, chemistry), ( biology ,biology)} be a relation defined in a different manner on A then the relation is
(a) Reflexive only
(b) Identity only
(c) Reflexive and identity only
(d) Neither reflexive nor Transitive only

C

Question. As library A has four different books that is n(A)= 4 then what will be no of reflexive relations that can be defined on
(a) 212
(b) 26
(c) 1
(d) None

A

Question. What will be the no of reflexive and symmetric relations that can be defined on B?
(a) 212
(b) 26
(c) 210
(d) None

B

There are two families, Family A and family B both the families have four members each

Family A

Family B

Daily expenses of each member of both the families are given in the table given below –
Let 𝑅1 = {(𝑅𝑖𝑐ℎ𝑎, 𝑅𝑒𝑒𝑡𝑎), (𝑅𝑖𝑡𝑒𝑠ℎ, 𝑅𝑎ℎ𝑢𝑙 )} be a relation on A and 𝑅2={(Arpita,Ankur) , (Arpita, Anjali), (Ankur, History) be a relation B.
On the basics of the information given above, answer the following:

Question. The relation on the family A is
(a) Reflexive only
(b) Symmetric only
(c) Reflexive and transitive
(d) Transitive only

D

Question. The relation on the family B is
(a) Reflexive only
(b) Symmetric only
(c) Reflexive and symmetric but not transitive
(d) Transitive but not symmetric

D

Question. Let {(Richa, Richa), ( Rita, Rita) (Ritesh, Ritesh), ( Rahul, Rahul)} be a relation defined in a different manner on the family A then the relation is
(a) Reflexive only
(b) Identity only
(c) Reflexive and identity only
(d) Neither reflexive nor Transitive only