JEE Questions for Maths Sets Relations And Functions Quiz 1 - MCQExams.com

If n(A) = 4 and n(B )= 6. Then, the number of one-one function from A to B is
  • 24
  • 60
  • 120
  • 360
Let R = {(a, a)} be a relation on set A. Then r is
  • Symmetric
  • Antisymmetric
  • Symmetric and antisymmetric
  • Neither symmetric nor anti – symmetric
Let R be the relation on the set R of all real numbers defined by a R iff |a – b| ≤ 1. Then R is
  • Reflexive and symmetric
  • Symmetric only
  • Transitive only
  • Anti – symmetric only
If A = { 4n - 3n -1: n ∈ N } and B = { 9(n -:n ∈ N }, then
  • B ⊂ A
  • A ∪ B = N
  • A ⊂ B
  • None of these
In a class of 60 students, if 25 students play cricket, 20 students play tennis and 10 students play both the games, then the number of students who play neither is
  • 45
  • 0
  • 25
  • 35
The set A = { x : x ∈ R, x2 = 16 and 2x = 6 } is equal to
  • ϕ
  • {14, 3, 4}
  • {3}
  • {4}
If A and B are two sets, then (A ∪ B)\' ∩ (A\' ∩ B) is equal to
  • A'
  • A
  • B'
  • None of these
If A = {1, 2}, B = { {1}, {2} }, C = { {1, 2} }. Then, which of the following relation is correct?
  • A = B
  • B ⊆ C
  • A ∈ C
  • A ⊂ C
If S = {1, 2, 3, 4}, then the total number of unordered pairs of disjoint subsets of S is
  • 25
  • 34
  • 42
  • 41
The shaded region in the figure represents
Maths-Sets Relations and Functions-49311.png
  • A ∩ B
  • A ∪ B
  • B - A
  • A - B
  • ( A - B )∪( B - A )
If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C, then
  • A = C
  • B = C
  • A ∩ B = ϕ
  • A = B
For any two sets A and B, A - (A - B) is equal to
  • B
  • A - B
  • A ∩ B
  • AC ∩ BC
If A and B are two sets, then (A ∪ B)' ∪ (A' ∩ B) is equal to
  • A'
  • A
  • B'
  • None of these
Three sets A,B and C are such that A=B ∩ C and B =C ∩ A, then
  • A ⊂ B
  • A ⊃ B
  • A = B
  • A ⊂ B'
In a class of 30 pupils, 12 take Chemistry, 16 take Physics and 18 take History. If all the 30 students take atleast one subject and no one take all three, then the number of pupils taking 2 subjects is
  • 16
  • 6
  • 8
  • 20
If A ⊆ B, then B ∪ A is equal to
  • B ∩ A
  • A
  • B
  • None of these
If Z is the set of integers. Then, the relation R= {(a, b) :1+ ab > 0} on Z is
  • reflexive and transitive but not symmetric
  • symmetric and transitive but not reflexive
  • reflexive and symmetric but not transitive
  • an equivalence relation
If f : R → R and is defined by
Maths-Sets Relations and Functions-49320.png

  • Maths-Sets Relations and Functions-49321.png
  • 2)
    Maths-Sets Relations and Functions-49322.png
  • (1, 2)
  • [1, 2]
The total number of subsets of a finite set A has 56 more elements than the total number of subsets of another finite set B. What is the number of elements in the set A?
  • 5
  • 6
  • 7
  • 8
The number of students who take both the subjects Mathematics and Chemistry is 30. This represents 10% of the enrolment in Mathematics and 12% of the enrolment in Chemistry. How many students take atleast one of these two subjects?
  • 520
  • 490
  • 560
  • 480
  • 540
There is a group of 265 persons who like either singing or dancing or painting. In this group, 200 like singing, 110 like dancing and 55 like painting. If 60 persons like both singing and dancing, 30 like both singing and painting and 10 like all three activities, then the number of persons who like only dancing and painting is
  • 10
  • 20
  • 30
  • 40
There are 100 students in a class. In the examination, 50 of them failed in Mathematics, 45 failed in Physics, 40 failed in Biology and 32 failed in exactly two of the three subjects. Only one student passed in all the subjects. Then, the number of students failing in all the three subjects
  • is 12
  • is 4
  • is 2
  • Cannot be determined
Out of 64 students, the number of students taking Mathematics is 45 and number of students taking both Mathematics and Biology is 10. Then, the number of students taking only Biology is
  • 18
  • 19
  • 20
  • None of these
If P = { θ : sinθ - cosθ = √2 cosθ } and Q = { θ : sinθ + cosθ = √2 sinθ } are two sets. Then,
  • P ⊂ Q and Q - P ≠ ϕ
  • Q ⊄ P
  • P ⊄ Q
  • P = Q
Two finite sets A and B have m and n elements, respectively. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m is
  • 7
  • 9
  • 10
  • 12
  • 13
For any two sets A and B, if A ∩ X = B ∩ X = ϕ and A ∪ X=B ∪ X for some set X, then
  • A - B = A ∩ B
  • A = B
  • B - A = A ∩ B
  • None of the above
If S is a set with 10 elements and A = {(x, y) : x, y ∈ S, x ≠ y}, then the number of elements in A is
  • 100
  • 90
  • 50
  • 45
In a certain town, 25% families own a cell phone, 15% families own a scooter and 65% families own neither a cell phone nor a scooter. If 1500 families own both a cell phone and a scooter, then the total number of families in the town is
  • 10000
  • 20000
  • 30000
  • 40000
  • 50000
A survey shows that 63% of the Americans like cheese whereas 76% like apples. If x % of the Americans like both cheese and apples, then
  • x = 39
  • x = 63
  • 39 ≤ x ≤ 63
  • None of these
If A = {1, 2, 3},B = {3, 4} and C = {4, 5, 6}, then A ∪ (B ∩ C) is equal to
  • {1, 2}
  • { ϕ }
  • {4, 5}
  • {1, 2, 3, 4}
If n(A) denotes the number of elements in the set A and if n(A )= 4, n(B) = 5 and n(A ∩ B) = 3, then n[(A x B) ∩ (B x A)] is equal to
  • 8
  • 9
  • 10
  • 11
The value of (A ∪ B ∪ C) (A ∩ BC ∩ CC)C ∩ CC is
  • B ∩ CC
  • BC ∩ CC
  • B ∩ C
  • A ∩ B ∩ C
Which of the following is correct?
  • A ∩ ϕ = A
  • A ∩ ϕ = ϕ
  • A ∩ ϕ = U
  • A ∩ ϕ = A'
If A= {1, 2, 3, 4} and B = {2, 4, 6}. Then, the number of set C such that A ∩ B ⊆ C ⊆ A ∪ B is
  • 6
  • 9
  • 8
  • 10
  • 12
If X and Y are the sets of all positive divisors of 400 and 1000, respectively (including 1 and the number). Then, n(X ∩ Y) is equal to
  • 4
  • 6
  • 8
  • 10
  • 12
If A = {x,y} then the power set of A is

  • Maths-Sets Relations and Functions-49341.png
  • 2)
    Maths-Sets Relations and Functions-49342.png

  • Maths-Sets Relations and Functions-49343.png

  • Maths-Sets Relations and Functions-49344.png
If n(A) = 4, n(B) = 3 and n(A × B × C) = 24, then n(C)is equal to
  • 288
  • 1
  • 12
  • 17
  • 2
The number of elements in the set {(a, b): 2a2 + 3b2 = 35, a, b ∈ Z}, where Z is the set of all integers, is
  • 2
  • 4
  • 8
  • 12
  • 16
{n(n + 1)(2n +: n ∈ Z}is a subset of
  • {6K : K ∈ Z}
  • {12K : K ∈ Z}
  • {18K : K ∈ Z}
  • {24K : K ∈ Z}
If R= {(3, 3), (6, 6), (9, 9), (12,12), (6, 12), (3, 9), (3,12), (3, 6)} is a relation on the set A= {3, 6, 9,12}. Then, the relation is
  • an equivalence relation
  • reflexive and symmetric
  • reflexive and transitive
  • only reflexive
If S is the set of all real numbers. A relation R has been defined on S by aRb ⇔ |a - b| then R is
  • symmetric and transitive but not reflexive
  • reflexive and transitive but not symmetric
  • reflexive and symmetric but not transitive
  • an equivalence relation
For any two real numbers θ and ϕ, we define θRϕ , if and only if sec2 θ - tan2ϕ =1. The relation R is
  • reflexive but not transitive
  • symmetric but not reflexive
  • both reflexive and symmetric but not transitive
  • an equivalence relation
If R is a relation on the set N, defined by {(x, y) : 2x - y = 10}, then R is
  • reflexive
  • symmetric
  • transitive
  • None of these
If R is the set of real numbers.Then,
Statement I A= {(χ, y) ∈ R × R : y - χ is an integer} is an equivalence relation on R.
Statement II B={(χ,y)∈ R x R : x= ay for some rational number α } is an equivalence relation on R.
  • Statement I is correct, Statement II is correct; Statement II is not a correct explanation for Statement I
  • Statement I is correct, Statement II is incorrect
  • Statement I is incorrect, Statement II is correct
  • Statement I is correct, Statement II is correct; Statement II is a correct explanation for Statement I
If A and B are two equivalence relations defined on set C, then
  • A ∩ B is an equivalence relation
  • A ∩ B is not an equivalence relation
  • A ∪ B is an equivalence relation
  • A ∪ B is not an equivalence relation
Consider the relations R = {(χ,y) | χ,y are real numbers and x = wy for some rational number w} S= {(m/n,p/q) | m, n, p and q are integers such that n, q ≠ 0 and qm = pn}. Then
  • R is an equivalence relation but S is not an equivalence relation
  • neither R nor S is an equivalence relation
  • S is an equivalence relation but R is not an equivalence relation
  • R and S both are equivalence relations
If A = {x, y, z} and B = {a, b, c,d}. Then, which one of the following is not a relation from A to B?
  • { (x, a), (x, c) }
  • { (y,c), (y,d) }
  • { (z, a), (z, d) }
  • { (z, b), (y,b), (a,d) }
  • { (x, c) }
If R and S are two non-void relations on a set A.Then, which of the following statements is incorrect?
  • R and S are transitive implies R n S is transitive
  • R and S are transitive implies R u S is transitive
  • R and S are symmetric implies R u S is symmetric
  • R and S are reflexive implies R n S is reflexive
If r is a relation from R (set of real numbers) to R defined by r = {(a, b) |a, b ∈ R and a - b + √3 is an irrational number} .Then, the relation r is
  • an equivalence relation
  • only reflexive
  • only symmetric
  • only transitive
If a relation R on the set N of natural numbers is defined as (χ, y) ⇔ χ2 - 4χy + 3y2 = 0, ∀ χ, y ∈ N. Then, the relation R is
  • reflexive
  • symmetric
  • transitive
  • an equivalence relation
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