Engineering Entrance Sample Papers

Sets, Relations, Functions Questions and Answers

Sets and Relations question

Sets and Relations JEE Mains:

Sets Relations and Functions JEE Mains Questions

Question 1
Let R be an equivalence relation on a finite set A having n elements. Then the number of ordered pairs in R is
A
Less than or equal to n
B
Greater than or equal to n
C
Less than n
D
None of these
Question 2
The relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is
A
Neither symmetric nor transitive
B
Reflexive but not transitive
C
Reflexive but not symmetric
D
Symmetric and Transitive
Question 3
Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. The relation is

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A
Reflexive only
B
Reflexive and transitive only
C
An equivalence relation
D
Reflexive and symmetric only
Question 4
Let S be the set of all real numbers. Then the relation R = {(a, b) : 1 + ab > 0} on S is

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A
Symmetric, transitive but not reflexive
B
Reflexive and symmetric but not transitive
C
Reflexive and transitive but not symmetric
D
Reflexive, transitive and symmetric
Question 5
Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is
A
A function
B
Transitive
C
Not symmetric
D
Reflexive
Question 6
Let A and B be two non-empty subsets of a set X such that A is not a subset of B, then
A
A and B are always disjoint
B
B is always a subset of A
C
A and the complement of B are always non-disjoint
D
A is always a subset of the complement of B
Question 7
In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is
A
22
B
45
C
10
D
33
Question 8
If A = {1, 2, 3, 4, 5}, then the number of proper subsets of A is
A
30
B
120
C
32
D
31
Question 9
The relation “less than” in the set of natural numbers is

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A
Only reflexive
B
Only transitive
C
Equivalence relation
D
Only symmetric
Question 10
The relation "is subset of" on the power set P(A) of a set A  is
A
Anti-symmetric
B
Symmetric
C
Equivalency relation
D
None of these
Question 11
The relation R defined on the set of natural numbers as {(a, b) : a differs from b by 3}, is given by
A
{(4, 1), (5, 2), (6, 3),.....}
B
{(1, 3), (2, 6), (3, 9),..}
C
{(1, 4, (2, 5), (3, 6),.....}
D
None of these
Question 12
Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m  and n  are

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A
7, 6
B
5, 1
C
8, 7
D
6, 3
Question 13
The number of non-empty subsets of the set {1, 2, 3, 4} is
A
15
B
17
C
14
D
16
Question 14
Let A and B be two non-empty subsets of a set X such that A is not a subset of B, then
A
B is always a subset of A
B
A is always a subset of the complement of B
C
A and the complement of B are always non-disjoint
D
A and B are always disjoint
Question 15
Let L be the set of all straight lines in the Euclidean plane. Two lines l1 and l2  are said to be related by the relation R i  is parallel to l2. Then the relation R is
A
Reflexive and Symmetric
B
Reflexive
C
Transitive and Equivalence
D
all
Question 16
Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m  and n  are
A
8, 7
B
5, 1
C
7, 6
D
6, 3
Question 17
Let A = {a, b, c} and B = {1, 2}. Consider a relation R  defined from set A to set B. Then R  is equal to set
A
B
B
A x B
C
B x A
D
A
Question 18
x2 = xy is a relation which is
A
None of these
B
Reflexive
C
Symmetric
D
Transitive
Question 19
Out of 800 boys in a school, 224 played cricket, 240 played hockey and 336 played basketball. Of the total, 64 played both basketball and hockey; 80 played cricket and basketball and 40 played cricket and hockey; 24 played all the three games. The number of boys who did not play any game is
A
128
B
240
C
216
D
160
Question 20
The number of proper subsets of the set {1, 2, 3} is
A
6
B
5
C
7
D
8
Question 21
Given the relation R = {(1, 2), (2, 3)} on the set A = {1, 2, 3}, the minimum number of ordered pairs which when added to R make it an equivalence relation is
A
6
B
8
C
7
D
5
Question 22
In a certain town 25% families own a phone and 15% own a car, 65% families own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard:
  1. 10% families own both a car and a phone
  2. 35% families own either a car or a phone
  3. 40,000 families live in the town
Which of the above statements are correct?
A
1 and 3
B
1, 2 and 3
C
1 and 2
D
2 and 3
There are 22 questions to complete.

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