Maths Class 12 MCQ Relations And Functions – Chapter 1

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Math Class 12 MCQ Relations And Functions – Chapter 1

Ques 1:

  • (2,4) ∈ R
  • (3,8) ∈ R
  • (6,8) ∈ R
  • (8,7) ∈ R

(6,8) ∈ R

Ques 2: Which of the following is not an equivalence relation on Z?

  • a R b ⇔ a+b is an even integer
  • a R b ⇔ a-b is an even integer
  • a R b ⇔ a<b
  • a R b ⇔ a = b

a R b ⇔ a<b

Ques 3: R is a relation on the set Z of integers and it is given by (x,y) ∈ R ⇔ |x-y|≤ 1. Then, R is

  • reflexive and transitive
  • reflexive and symmetric
  • symmetric and transtitive
  • an equivalence relation

reflexive and symmetric

Ques 4: The relation R defined on the set A = {1,2,3,4,5} by R = {(a,b):|a2-b2|<16}, is given by

  • {(1,1),(2,1),(3,1),(4,1),(2,3)}
  • {(2,2),(3,2),(4,2),(2,4)}
  • {(3,3),(4,3),(4,3),(5,4),(3,4)}
  • none of these

none of these

Relations and Functions Class 12 Maths MCQs

Ques 5: Let R be the relation over the set of all straight lines in a plane such that l1 R l2 ⇔ l1 ⊥ l2. Then, R is

  • symmetric
  • reflexive
  • transitive
  • an equivalence relation

symmetric

Ques 6: If A = {a,b,c}, then the relation R = {(b,c)} on A is

  • reflexive only
  • symmetric only
  • transitive only
  • reflexive and transitive only

transitive only

Ques 7: Let = {2,3,5,….., 17,18}. ‘≈’ be the equivalence relation and A × A, cartesian product of A with itself, defined by (a,b) ≈ (c,b) iff ad = bc. Then, the number of ordered pairs of the equivalence class of (3,2) is

  • 4
  • 5
  • 6
  • 7

6

Ques 8: Let A {1,2,3}. Then, the number of relations containing (1,2) and (1,3) which are reflexive and symmetric but not transitive is

  • 1
  • 2
  • 3
  • 4

1

Ques 9: The relation ‘R’ in N×N such that (a,b) R (c,d) ⇔ a+d = b+c is

  • reflexive but not symmetric
  • reflexive and transitive but not symmetric
  • an equivalence relation
  • none of these

an equivalence relation

Ques 10: If A = {1,2,3}, B = {1,4,6,9} and R is a relation from A to B defined by ‘x is greater they y’. The range of R is

  • {1,4,6,9}
  • {4,6,9}
  • {1}
  • {2,3,4,5}

{1}

Ques 11: A relation R is defined from {2,3,4,5} to {3,6,7,10} by x y ⇔ x is relatively prime to y. Then domain of R is

  • {2,3,5}
  • {3,5}
  • {2,3,4}
  • {2,3,4,5}

{2,3,4,5}

Ques 12: A relation ∅ from C to R is defined by x ∅ y ⇔ |x| = y. Which one is correct?

  • (2+3 i) ∅ 13
  • 3 ∅ (-3)
  • (1+i) ∅2
  • i ∅ 1

i ∅ 1

MCQ Questions for Class 12 Maths Chapter 1 Relations and Functions

Ques 13: Let R be a relation on N defined by x + 2y = 8. The domain of R is

  • {2,4,8}
  • {2,4,6,8}
  • {2,4,6}
  • {1,2,3,4}

{2,4,6}

Ques 14: R is a relation from (11,12,13) to {8,10,12} defined by y = x-3. Then, R-1 is

  • {(8,11), (10,13)}
  • {(11,8),(13,10)}
  • {(10,13),(8,11),(8,10)}
  • none of these

{(8,11), (10,13)}

Ques 15: Let R = {)a,a),(b,b),(c,c),(a,b)} be a relation on set A = {a,b,c}. Then, R is

  • identity relation
  • reflexive
  • symmetric
  • equivalence

reflexive

Ques 16: Let A = {1,2,3} and R = {(1,2),(2,3),(1,3) be a relation on A. Then, R is

  • neither reflexive nor transitive
  • neither symmetric nor transitive
  • transitive
  • none of these

transitive

Ques 17: If R is the largest equivalence relation on a set A and S is any relation on A, then

  • R ⊏ S
  • S ⊏ R
  • R = S
  • none of these

S ⊏ R

Ques 18: If R a relation on the set A = {1,2,3,4,5,6,7,8,9} given by x R y ⇔ y = 3x, then R =

  • {(3,1),(6,2),(8,2),(9,3)
  • {(3,1),(6,2),(9,3)}
  • {(3,1),(2,6),(3,9)}
  • none of these

none of these

Ques 19: If R is a relation on the set A = {1,2,3} given by R = (1,1),(2,2),(3,3), then R is

  • reflexive
  • symmetric
  • transitive
  • all the three options

all the three options

Ques 20: If A = {a,b,c,d}, then a relation R = {(1,b),(b,a),(a,a)} on A is

  • symmetric and transitive only
  • reflexive and transitive only
  • symmetric only
  • transitive only

symmetric only/p>

Ques 21: If A = {1,2,3), then a relation R = {{2,3)} on A is

  • symmetric and transitive only
  • transitive only
  • symmetric only
  • i ∅ 1

symmetric only

Solved MCQ Questions for Class 12 Maths Chapter 1 Relations and Functions

Ques 22: Let R be the relation on the set A = {1,2,3,4} given by R = {(1,2),(2,2),(1,1),(4,4),(1,3),(3,3),(3,2)} Then,

  • R is reflexive and symmetric but not transitive
  • R is reflexive and transitive but not symmetric
  • R is symmetric and transitive but not reflexive
  • R is an equivalence relation

R is reflexive and transitive but not symmetric

Ques 23: Let A = {1,2,3}. Then, the number of equivalence relation containing (1,2) is

  • 1
  • 2
  • 3
  • 4

2

Ques 24: The relation R = {1,1),(2,2),(3,3)} on the set {1,2,3} is

  • symmetric only
  • reflexive only
  • an equivalence relation
  • transitive only

an equivalence relation

Ques 25: S is a relation over the set R of all real numbers and it is given by (a,b) ∈ S ⇔ ab ≥ 0.

  • symmetric and transitive only
  • reflexive and symmetric only
  • antisymmetric relation
  • an equivalence relation

reflexive and symmetric only

Ques 26: In the set Z of all integers, which of the following relation R is not an equivalence relation?

  • x R y : if x ≤ y
  • x R y : if x = y
  • x R y : if x-y is an even integer
  • x R y : if x ≡ y (mod 3)

x R y : if x ≤ y

Ques 27: Let A = {1,2,3} and consider the relation R = {(1,1),(2,2),(3,3),(1,2),(2,3)(1,2)}. Then, R is

  • reflexive but not symmetric
  • reflexive but not transitive
  • symmetric and transitive
  • neither symmetric nor transitive

reflexive but not symmetric

Ques 28: The relation S defined on the set R of all real number by the rule a Sb iff a ≥ b is

  • an equivalence relation
  • reflexive, transitive but not symmetric
  • symmetric, transitive but not reflexive
  • neither transitive nor reflexive but symmetric

reflexive, transitive but not symmetric

Ques 29: The maximum number of equivalence relation on the set A = {1,2,3} is

  • 1
  • 2
  • 3
  • 5

5

Ques 30: Let R be a relation on the set N of all straight lines in a plane. Let a relation R be defined by lR m iff l is

  • Reflexive and symmetric
  • Transitive and symmetric
  • Equivalaence
  • Reflexive, transitive but not symmetric

Reflexive, transitive but not symmetric

Ques 31: Let L denote the set of all straight lines in a plane. Let a relation R be defined by lR m iff l is perpendicular to m for all l, m ∈ L. Then, R is

  • reflexive
  • symmetric
  • transitive
  • none of these

symmetric

Ques 32: Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as a R b if a is congruent to b for all a,b ∈ T. then, R is

  • reflexive but not symmetric
  • transitive but not symmetric
  • equivalence
  • none of these

equivalence

Ques 33: Consider a non-empty set consisting of children in a family and relation R defined as a Rb if a is brother of b. Then, R is

  • symmetric but not transitive
  • transitive but not symmetric
  • neither symmetric not transitive
  • both symmetric and transitive

transitive but not symmetric

Ques 34: For real numbers x and y, define x R y iff x-y + √2 is an irrational number. Then the relation R is

  • reflexive
  • symmetric
  • transitive
  • none of these

reflexive

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These MCQs on Relations and Functions are prepared keeping in mind the latest pattern of examination in mind. These questions are really important from your examination point of view and will help you a lot in scoring good marks. So, practice them as many times as you want and score good marks in class 12 maths examination. Enjoy Learning.

Updated: December 4, 2021 — 3:00 pm

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