CBSE Class 12 Mathematics Relations And Functions Assignment Set B

Question. If X = {8ⁿ – 7 – 1: n ∈ N): n∈N} and Y = {49(n–1): n∈N} then:
a. X ⊆ Y
b. Y ⊆ X
c. X = Y
d. None of these
Answer : A

Question. If A and B are any two sets, then A ∪ (A ∩ B) is equal to:
a. A
b. B
c. c A
d. c B
Answer : A

Question. The set of intelligent students in a class is:
a. A null set
b. A singleton set
c. A finite set
d. Not a well defined collection
Answer : D

Question. Given the sets A = {1, 2, 3}, B = {3, 4} , C = {4, 5, 6}, then: A ∪ (B ∩ C) is
a. {3}
b. {1, 2, 3, 4}
c. {1, 2, 4, 5}
d. {1, 2, 3, 4, 5, 6}
Answer : B

Question. If A ⊆ B , then A ∪ B is equal to:
a. A
b. B ∩ A
c. B
d. None of these
Answer : C

Question. In a city 20 percent of the population travels by car, 50 percent travels by bus and 10 percent travels by both car and bus. Then persons travelling by car or bus is:
a. 80 percent
b. 40 percent
c. 60 percent
d. 70 percent
Answer : C

Question. If the sets A and B are defined as A = {(x, y) : y 1/x, 0 ≠ x ∈ R} B = {(x, y) : y = −x, x ∈ R} , then:
a. A ∩B = A
b. A ∩ B = B
c. A ∩ B =φ
d. None of these
Answer : C

Question. Let A = [x : x ∈ R, |x| < 1] B = [x : x ∈ R, |x – 1| ≥ 1] and A ∪ B = R − D, then the set D is:
a. [x : 1 < x ≤ 2]
b. [x : 1 ≤ x < 2]
c. [x : 1 ≤ x ≤ 2]
d. None of these
Answer : B

Question. If A,B and C are non-empty sets, then (A–B) ∪ (B – A) equals?
a. (A ∪ B) – B
b. A – (A ∩ B)
c. (A ∪ B) – (A ∩ B)
d. (A ∩ B) ∪ (A ∪ B)
Answer : C

Question. Which of the following is the empty set?
a. {x : x is a real number and x² −1 = 0}
b. {x : x is a real number and x² +1 = 0}
c. {x : x is a real number and x² − 9 = 0}
d. {x : x is a real number and x² = x + 2}
Answer : B

Question. If the sets A and B are defined as:
A = {(x, y) : y = e^x , x∈R}
B = {(x, y) : y = x, x∈ R}, then
a. B ⊆ A
b. A ⊆ B
c. A ∩ B =φ
d. A ∪ B = A
Answer : C

Question. If X = {4ⁿ – 3n – 1 : n ∈ N} and Y ={9(n – 1) : n ∈ N} then X ∪ Y is equal to:
a. X
b. Y
c. N
d. None of these
Answer : B

Question. In a class of 55 students, the number of students studying different subjects are 23 in mathematics, 24 in physics, 19 in chemistry, 12 in mathematics and physics, 9 in mathematics and chemistry, 7 in physics and chemistry and 4 in all the three subjects. The number of students who have taken exactly one subject is:
a. 6
b. 9
c. 7
d. 5
Answer : D

Question. If A,B and C are any three sets, then A×(B∩C) is equal to:
a. (A × B) ∪ (A × C)
b. (A × B) ∩ (A × C)
c. (A ∪ B) × (A ∪ C)
d. (A ∩ B) × (A ∩ C)
Answer : B

Question. Given two finite sets A and B such that n(A) = 2, n(B) = 3.
Then total number of relations from A to B is?
a. 4
b.8
c. 64
d. 9
Answer : C

Question. If A = {2, 4, 5}, B = {7, 8, 9}, then n(A× B) is equal to:
a. 6
b. 9
c. 3
d. 0
Answer : B

Question. In a town of 10,000 families it was found that 40% family buy newspaper A, 20% buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then number of families which buy: A only is
a. 3100
b. 3300
c. 2900
d. 1400
Answer : B

Question. If P, Q and R are subsets of a set A, then R×(P^cUQ^c)c =?
a. (R × P) ∩ (R × Q)
b. (R × Q) ∩ (R × P)
c. (R × P) ∪ (R × Q)
d. None of these
Answer : A, B

Question. If the set A has p elements, B has q elements, then the number of elements in A × B is:
a. p + q
b. p + q + 1
c. pq
d. p²
Answer : C

Question. With reference to a universal set, the inclusion of a subset in another, is relation, which is?
a. Symmetric only
b. Equivalence relation
c. Reflexive only
d. None of these
Answer : D

Question. Let A = {1, 2, 3}. The total number of distinct relations that can be defined over A is:
a. 9 2
b. 6
c. 8
d. 5
Answer : A

Question. Let X = {1, 2, 3, 4,5} and Y = {1, 3,5, 7, 9} . Which of then following is/are relations from X to Y?
a. R₁ = {(x, y) | y = 2 + x, x∈ X, y∈Y}
b. R₂ = {(1,1), (2,1), (3, 3), (4, 3), (5, 5)}
c. R₃ = {(1,1), (1, 3)(3, 5), (3, 7), (5, 7)}
d. R₄ = {(1, 3), (2, 5), (2, 4), (7, 9)}
Answer : ABC

Question. Let X be a family of sets and R be a relation on X defined by ‘A is disjoint from B’. Then R is:
a. Reflexive
b. Symmetric
c. Anti-symmetric
d. Transitive
Answer : B

Question. Let A = {1, 2, 3}, B = {1, 3, 5}. A relation R : A → B is defined by R = {(1, 3), (1, 5), (2, 1)}. Then −1 R is defined by:
a. {(1,2), (3,1), (1,3), (1,5)}
b. {(1, 2), (3, 1), (2, 1)}
c. {(1, 2), (5, 1), (3, 1)
d. None of these
Answer : C

Question. The relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is:
a. Reflexive but not symmetric
b. Reflexive but not transitive
c. Symmetric and Transitive
d. Neither symmetric nor transitive
Answer : A

Question. Let R and S be two non-void relations on a set A. Which of the following statements is false:
a. R and S are transitive ⇒ R ∪ S is transitive
b. R and S are transitive ⇒ R ∩ S is transitive
c. R and S are symmetric ⇒ R ∪ S is symmetric
d. R and S are reflexive ⇒ R ∩ S is reflexive
Answer : A

Question. Let P = {(x, y) | x² + y² = 1, x, y∈R} .Then P is:
a. Reflexive
b. Symmetric
c. Transitive
d. Anti-symmetric
Answer : B

Question. Let R be a relation on the set N of natural numbers defined 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. The solution set of 8 x ≡ 6(mod 14), x ∈ Z , are:
a. [8] ∪ [6]
b. [8] ∪ [14]
c. [6] ∪ [13]
d. [8] ∪ [6] ∪ [13]
Answer : C

  

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