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This mock test of Test: Sets 2 for JEE helps you for every JEE entrance exam.
This contains 25 Multiple Choice Questions for JEE Test: Sets 2 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

If n (A) = 3 and n (B) = 6 and A ⊆ B, then the number of elements in A ∪ B is equal to

Solution:

Since, A ⊆ B

A ∪ B = B

n(A ∪ B) = n(B) = 6

QUESTION: 2

If n (A) = 3 and n (B) = 6 and A ⊆ B, then the number of elements in A ∩ B is equal to

Solution:

QUESTION: 3

Let A and B be subsets of a set X, Then which of the following is correct

Solution:

A – B is All elements of A minus elements of B

B’ contains all elements of X except elements of B

So, A – B = A ∩ B’

QUESTION: 4

If A , B and C are any three sets, then A – (B ∪ C) is equal to

Solution:

In set theory, 'U' is analogous to '+'.

A - (B ∪ C) = (A - B) ∩ (A - C)

QUESTION: 5

What is the cardinality of the set of odd positive integers less than 10?

Solution:

Set S of odd positive an odd integer less than 10 is {1, 3, 5, 7, 9}. Then, Cardinality of set S = |S| which is 5.

QUESTION: 6

If A, B and C are any three sets, then A ∩ (B ∪ C) is equal to

Solution:

Distributive property in set theory: The union and intersection of sets may be seen as analogous to the addition and multiplication of numbers.

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

QUESTION: 7

If aN = {ax : x ∈ N}, then the set 3N ∩ 7N is

Solution:

The condition states that aN, So V can relate it to 3n... and the multiples of 3n is 3, 6, 9, 12...etc and similarly multiples of 7n is 7,14, 21, 28...etc when taken the commom out we see that the common is 21, 42, 63..etc which are the multiples of 21.

QUESTION: 8

The smallest set A such that A ∪ {1, 2} = {1, 2, 3, 5, 9} is

Solution:

QUESTION: 9

If A and B are sets, then A ∩ (B – A) is

Solution:

A, B are sets

B – A = B – (A ∩ B)

A ∩ (B – A) = A ∩ (B – (A ∩ B)) = Φ

QUESTION: 10

If A = {0,1,5, 4, 7}. Then the total number subsets of A are

Solution:

QUESTION: 11

If A and B be two sets such that n (A) = 70, n (B) = 60, and n (A ∪ B) = 110. Then n (A ∩ B) is equal to

Solution:

QUESTION: 12

Which set is the subset of all given sets?

Solution:

The question should be: “Which set is the subset of all the sets?”

Φ = { } (Empty set) is a subset of all the sets.

QUESTION: 13

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in A U B

Solution:

**We know that**

**n(A∪B)=n(A)+n(B)−n(A∩B)......(i)**

**n(A∪B)=n(A)+n(B)-n(A∩B)......(i)**

**Case 1 From (i) , it is clear that n(A∪B)**

**n(A∪B) will be maximum when n(A∩B)=0**

**In that case, **

**n(A∪B)=n(A)+n(B)=(3+6)=9**

**∴ Maximum number of elements in **

**(A∪B)=9**

**Case 2 From (i) , it is clear that n(A∪B)**

**n(A∪B) will be minimum when n(A∩B)=0 maximum ,i.e, when **

**n(A∩B)=3**

**In this case, **

**n(A∪B)=n(A)+n(B)−n(A∩B)=(3+6−3)=6**

**∴ minimum number of elements in **

**A∪B=6**

QUESTION: 14

If A = {x : x ≠ x} represents

Solution:

QUESTION: 15

If A = {x : x^{2} − 5x + 6 = 0}, B = {2, 4}, C = {4, 5}, then A × (B ∩ C) is

Solution:

Clearly, A = {2, 3}, B = {2, 4}, C = {4,5} B ∩ C = {4}

∴ A × (B ∩ C) = {(2, 4), (3, 4)}.

QUESTION: 16

Which of the following is a set

Solution:

QUESTION: 17

Let A = {x : x ∈ R, |x| < 1}; B = {x : x ∈ R, |x − 1| ≥ 1} and A ∪ B = R − D, then the set D is (R ∈ Set of real numbers)

Solution:

A = {x : x ∈ R,−1 < x < 1}

B = {x : x ∈ R : x − 1 ≤ −1 or x − 1 ≥ 1]

= {x : x ∈ R : x ≤ 0 or x ≥ 2}

∴A ∪ B = R − D , where D = [x : x ∈ R,1 ≤ x < 2]

QUESTION: 18

If A, B and C are non-empty sets, then (A - B) U (B - A) equals

Solution:

Use venn diagram approach

QUESTION: 19

Which of the following statements is true?

Solution:

Since the curly brackets denote a set, so the other three options are a subset of the set {1, 2, 3} and and only 3 belongs to the set.

QUESTION: 20

If a set A has n elements, then the total number of subsets of A is

Solution:

QUESTION: 21

If A, B, C be any three sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C, then

Solution:

WKT, A ∩ B = A ∩ C

A Ս B = A Ս C

A + B - A ∩ B = A + C - A ∩ C

B + (A ∩ B - A ∩ C) = C

B = C

QUESTION: 22

Given the sets A = {1, 2, 3}, B = {3 , 4}, C = {4 , 5, 6}, then A ∪ (B ∩ C) is

Solution:

QUESTION: 23

If A = {a, b}, B = {c, d}, C = {d, e}, then {(a, c), (a, d),(a, e), (b, c), (b, d), (b, e)} is equal to

Solution:

QUESTION: 24

Two finite sets have m and n elements. The total number of subsets of the first set is 48 more than the total number of subsets of the second set. The values of m and n are

Solution:

Total number of subsets of the first set = 2^{m}

Total number of subsets of the second set = 2^{n}

2^{m} = 2^{n} + 48

By hit and trial,

m = 6, n = 4

QUESTION: 25

Let A = {x : x is a prime factor 240} and B = {x : x is the sum of any two prime factors of 240}. Then

Solution:

A = {2, 5, 3} and B = {7, 8, 5} and A ∪ B = {2, 3, 5, 7, 8}

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