CBSE Class 12 Mathematics Relation And Function Worksheet Set 01

Question. Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is:
(a) Reflexive and symmetric
(b) Transitive and symmetric
(c) Equivalence
(d) Reflexive, transitive but not symmetric.
Answer. D

Question. If the set A contains 7 elements and set B contains 10 elements, then the number of one-one functions from A to B is :
(a) ¹⁰C₇
(b) ¹⁰C₇ × 7!
(c) 7¹⁰
(d) 10⁷
Answer. B

Question. Let N be the set of natural numbers and the function f : N → N be defined by f(n) = 2n + 3 ∀ ∈ N. Then f is
(a) surjective
(b) injective
(c) bijective
(d) none of these
Answer. B

Question. Set A has 3 elements and the set B has 4 elements.
Then the number of injective mappings that can be defined from A to B is:
(a) 144
(b) 12
(c) 24
(d) 64
Answer. C

Question. If A = {a, b, c} and B = {4, 5, 6}, then number of functions from A to B is :
(a) 9
(b) 27
(c) 18
(d) 81
Answer. B

Question. Let f : R → R be defined by f(x) = x² + 1. Then, preimages of 17 and – 3, respectively, are:
(a) φ, {4, – 4}
(b) {3, – 3}, φ
(c) {4, – 4}, φ
(d) {4, – 4}, {2, – 2}
Answer. C

Question. For real numbers x and y, define xRy if and only if x – y + 2 is an irrational number. Then the relation R is:
(a) reflexive
(b) symmetric
(c) transitive
(d) none of these
Answer. A

Question. Let A = {2, 3, 6}. Which of the following relations on A are reflexive?
(a) R = {(2, 2), (3, 3), (6, 6)}
(b) R = {(2, 2), (3, 3), (3, 6), (6, 3)}
(c) R = {(2, 2), (3, 6), (2, 6)}
(d) None of these
Answer. A

Question. Let R be the relation on N defined by R = {(x, y): x + 2y = 8}. Then, the domain of R is:
(a) {2, 4, 6, 8}
(b) {2, 4, 8}
(c) {2, 4, 6}
(d) {1, 2, 3, 4}
Answer. C

Question. The relation R in the set of natural numbers N defined as R = {(x, y) : y = x + 5 and x < 4} is :
(a) reflexive
(b) symmetric
(c) transitive
(d) None of these
Answer. D

Question. For the set A = {1, 2, 3}, define a relation R in the set A as follows
R = {(1, 1), (2, 2), (3, 3), (1, 3)}
Then, the ordered pair to be added to R to make it the smallest equivalence relation is :
(a) (1, 3)
(b) (3, 1)
(c) (2, 1)
(d) (1, 2)
Answer. B

Question. If A = {x ∈ Z : 0 ≤ x ≤ 12} and R is the relation in A given by R = {(a, b) : a = b). Then, the set of all elements related to 1 is :
(a) {1, 2}
(b) {2, 3}
(c) {1}
(d) {2}
Answer. C

Question. f : X → Y is onto, if and only if :
(a) range of f = Y
(b) range of f ≠ Y
(c) range of f < Y
(d) range of f ≥ Y
Answer. A

Question. The number of all one-one functions from set A = {1, 2, 3} to itself is :
(a) 2
(b) 6
(c) 3
(d) 1
Answer. B

Question. Let 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
Answer. B

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
Answer. C

Question. The greatest integer function f : R → R, given by f(x) = [x] is :
(a) one-one
(b) onto
(c) both one-one and onto
(d) neither one-one nor onto
Answer. B

Question. Set A has 3 elements and the set B has 4 element then the total number of injective mapping :
(a) 144
(b) 12
(c) 24
(d) 64
Answer. C

Question. The relation of the relation R = {(x, x²) : x is a prime number less than 13} :
(a) {2, 3, 5, 7}
(b) {4, 9, 25, 49, 121}
(c) {2, 3, 5, 7, 11}
(d) {1, 4, 9, 25, 49, 121}
Answer. B

Question. Let f : R → R be defined by f(x) = (x^2-8)/(x²+2), then f is :
(a) One-one but not onto
(b) One-one and onto
(c) Onto but not one-one
(d) Neither one-one nor onto
Answer. D

Question. Let R be the relation on the set A = {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (3, 3), (2, 3), (1, 3)}. then :
(a) R is reflexive and symmetric but not transitive
(b) R is reflexive and transitive but not symmetric
(c) R is symmetric and transitive but not reflexive
(d) R is an equivalance relation
Answer. B

Question. R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x – 3 then R– 1 is :
(a) {(8, 11), (10, 13)}
(b) {(11, 8), (13, 10)}
(c) {(10, 13), (8, 11), (8, 10)}
(d) None of these
Answer. A

Question. Which one of the following is an identity relation?
(a) (1, 2), (2, 3), (1, 3)
(b) (5, 5), (4, 4), (2, 2)
(c) (1, 3), (3, 1), (2, 3)
(d) None of these
Answer. 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 for all a, b Î T, then R is :
(a) Reflexive but not symmetric
(b) Transitive but not symmetric
(c) Equivalence
(d) Neither symmetric nor transitive
Answer. C

Question. One-one, onto function is also called :
(a) Injective function
(b) Surjective function
(c) Bijective function
(d) All of these
Answer. C

Question. The relation R on R defined by R = {(a, b) : a £ b3} is :
(a) Reflexive
(b) Symmetric
(c) Transitive
(d) None of these
Answer. D

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

Question. Let us define a relation R in R as a 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 A = {1, 2, 3} and consider the relation R = {(1, 1),(2, 2), (3, 3), (1, 2), (2, 3)}
Then R is : 
(a) reflexive but not symmetric
(b) reflexive but not transitive
(c) symmetric and transitive
(d) niether symmetric nor transitive
Answer. A

Question. 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)}.
Choose the correct answer.
(a) R is reflexive and symmetric but not transitive
(b) R is reflexive and transitive but not symmetric
(c) R is symmetric and transitive but not reflexive
(d) R is an equivalence relation
Answer. B

Case Based Questions

Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x – 4.
Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Answer the following using the above information:

Question. Let relation R be defined by R = {(L₁, L₂) : L₁ || L₂ where L₁, L₂ ∈ L}, then R is ____ relation.
(a) Equivalence
(b) Only reflexive
(c) Not reflexive
(d) Symmetric but not transitive
Answer : A

Question. Let f : R → R be defined by f(x) = x – 4. Then the range of f(x) is ______ .
(a) R
(b) Z
(c) W
(d) Q
Answer : A

Question. Let R = {(L₁, L₂) : L₁ ⊥ L₂ where L₁, L₂ ∈ L} which of the following is true?
(a) R is Symmetric but neither reflexive nor transitive.
(b) R is Reflexive and transitive but not symmetric
(c) R is Reflexive but neither symmetric nor transitive.
(d) R is an Equivalence relation.
Answer : A

Question. Let R = {(L₁, L₂) : L₁ is parallel to L₂ and L₁ : y = x – 4} then which of the following can be taken as L₂?
(a) 2x – 2y + 5 = 0
(b) 2x + y = 5
(c) 2x + 2y + 7 = 0
(d) x + y = 7
Answer : A

Question. The function f : R → R defined by f(x) = x – 4 is _______ .
(a) Bijective
(b) Surjective but not injective
(c) Injective but not Surjective
(d) Neither Surjective nor Injective
Answer : A

A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever
Let I be the set of all citizens of India who were eligible to exercise their voting right in general election held in 2019. A relation ‘R’ is defined on
I as follows:
R = {(V₁, V₂)} : V₁, V₂ ∈ I and both use their voting right in general election — 2019}

Based on the above information answer the following:

Question. Two neighbours X and Y ∈ I. X exercised his voting right while Y did not cast her vote in general election — 2019. Which of the following is true?
(a) (X, Y) ∈ R
(b) (Y, X) ∈ R
(c) (X, X) ∉ R
(d) (X, Y) ∉ R
Answer : D

Question. The above defined relation R is ............. .
(a) Symmetric and transitive but not reflexive
(b) Universal relation
(c) Equivalence relation
(d) Reflexive but not symmetric and transitive
Answer : C

Question. Three friends F₁, F₂ and F₃ exercised their voting right in general election — 2019, then which of the following is true?
(a) (F₁, F₂) ∈ R, (F₂, F₃) ∈ R and (F₁, F₃) ∈ R
(b) (F₁, F₂) ∈ R, (F₂, F₃) ∈ R and (F₁, F₃) ∉ R
(c) (F₁, F₂) ∈ R, (F₂, F₃) ∈ R but (F₁, F₃) ∉ R
(d) (F₁, F₂) ∉ R, (F₂, F₃) ∉ R and (F₁, F₃) ∉ R
Answer : A

Question. Mr. Shyam exercised his voting right in General Election — 2019, then Mr. Shyam is related to which of the following?
(a) All those eligible voters who cast their votes
(b) Family members of Mr. Shyam
(c) All citizens of India
(d) Eligible voters of India
Answer : A

Question. Mr. ‘X’ and his wife ‘W’ both exercised their voting right in general election — 2019, which of the following is true?
(a) Both (X, W) and (W, X) ∈ R
(b) (X, W) ∈ R but (W, X) ∉ R
(c) Both (X, W) and (W, X) ∉ R
(d) (W, X) ∈ R but (X, W) ∉ R
Answer : A

Please click on below link to download CBSE Class 12 Mathematics Relation And Function Worksheet Set A