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Test: Sets- 1 - CA Foundation MCQ


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30 Questions MCQ Test - Test: Sets- 1

Test: Sets- 1 for CA Foundation 2024 is part of CA Foundation preparation. The Test: Sets- 1 questions and answers have been prepared according to the CA Foundation exam syllabus.The Test: Sets- 1 MCQs are made for CA Foundation 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Sets- 1 below.
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Test: Sets- 1 - Question 1

Choose the most appropriate option or options (a), (b) (c) and (d)

The number of subsets of the set {2, 3, 5} is 

Detailed Solution for Test: Sets- 1 - Question 1

The subsets of set are:

{ (),(2),(3),(5),(2,3),(2,5),(3,5),(2,3,5) }
Total eight subsets.

Shortcut to find number of subsets:
2n
where n = no.of elements in a set.

Applying this shortcut in the above set,
n=3

2= 8

Test: Sets- 1 - Question 2

The number of subsets of a set containing n elements is

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Test: Sets- 1 - Question 3

The null set is represented by

Test: Sets- 1 - Question 4

A = {2, 3, 5, 7} , B { 4, 6, 8, 10} then A ∩ B can be written as

Test: Sets- 1 - Question 5

The set {x|0<x<5} represents the set when x may take integral values only

Test: Sets- 1 - Question 6

The set {0, 2, 4, 6, 8, 10} can be written as

Test: Sets- 1 - Question 7

If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} then find the number of proper subsets of A ∩  B ?

Detailed Solution for Test: Sets- 1 - Question 7

CALCULATION:

Given: A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9}

As we know that, A ∩ B = {x : x ∈ A and x ∈ B}

⇒ A ∩ B = {2, 4, 7, 9}

As we can see that,

The number of elements present in A ∩ B = 4

i.e n(A ∩ B) = 4

As we know that;

If A is a non-empty set such that n(A) = m then

The numbers of proper subsets of A are given by 2m - 1.

So, The number of proper subsets of A ∩  B = 24 - 1 = 15

Hence, the correct option is 2

Test: Sets- 1 - Question 8

If P = {1, 2, 3, 5, 7}, Q = {1, 3, 6, 10, 15}, Universal Set S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

Q. The cardinal number of P ∪ Q is

Test: Sets- 1 - Question 9

If P = {1, 2, 3, 5, 7}, Q = {1, 3, 6, 10, 15}, Universal Set S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

Q. n(P∩Q) is 

Detailed Solution for Test: Sets- 1 - Question 9

Explanation:

Intersection of Sets:
- The intersection of two sets P and Q, denoted by P ∩ Q, is the set of elements that are common to both sets.
- In this case, P = {1, 2, 3, 5, 7} and Q = {1, 3, 6, 10, 15}.
- To find the intersection, we look for elements that are present in both sets.
- The common elements between P and Q are 1 and 3.

Calculation:
- n(P ∩ Q) = Number of elements in the intersection of sets P and Q.
- n(P ∩ Q) = 2 (as there are 2 common elements: 1 and 3).

Therefore, the correct answer is A: 2.

Test: Sets- 1 - Question 10

If P = {1, 2, 3, 5, 7}, Q = {1, 3, 6, 10, 15}, Universal Set S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

Q. n(S-Q) is 

Test: Sets- 1 - Question 11

The set of cubes of the natural number is

Test: Sets- 1 - Question 12

The set {2x|x is any positive rational number } is

Test: Sets- 1 - Question 13

{1– (–1)x} for all integral x is the set

Test: Sets- 1 - Question 14

E is a set of positive even number and O is a set of positive odd numbers, then E ∪ O is a

Test: Sets- 1 - Question 15

If R is the set of positive rational number and E is the set of real numbers then

Test: Sets- 1 - Question 16

If N is the set of natural numbers and I is the set of positive integers, then

Test: Sets- 1 - Question 17

If I is the set of isosceles triangles and E is the set of equilateral triangles, then

Detailed Solution for Test: Sets- 1 - Question 17

Since every equilateral triangle is also an isoceles triangle then E is a subset of I.

Test: Sets- 1 - Question 18

If R is the set of isosceles right angled triangles and I is set of isosceles triangles, then

Detailed Solution for Test: Sets- 1 - Question 18

If R is the set of isosceles right angled triangles and l is set of isosceles triangles, then R belongs to l.

 (R is a subset of l) 

Test: Sets- 1 - Question 19

{n(n+1)/2 : n is a positive integer} is

Test: Sets- 1 - Question 20

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 }; find A ∪ B 

Test: Sets- 1 - Question 21

A ∪ A is equal to

Test: Sets- 1 - Question 22

(A ∪ B)' is equal to

Test: Sets- 1 - Question 23

(A ∩ B)' is equal to

Test: Sets- 1 - Question 24

A ∪ E is equal to (E is a superset of A)

Test: Sets- 1 - Question 25

A ∩ E (E is a superset of A) is equal to

Test: Sets- 1 - Question 26

E ∪ E is equal to

Test: Sets- 1 - Question 27

A ∩ E' is equal to

Test: Sets- 1 - Question 28

If P = {1, 2, 3, 5, 7}, Q = {1, 3, 6, 10, 15}, Universal Set S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
The cardinal number of P ∩ Q is

Detailed Solution for Test: Sets- 1 - Question 28

P = {1, 2, 3, 5, 7}, Q = {1, 3, 6, 10, 15},
P ∩ Q = { 1, 3 }.
The cardinal number is the number of elements of a set.
So The cardinal number of P ∩ Q is 2.

Test: Sets- 1 - Question 29

A ∩ A' is equal to

Test: Sets- 1 - Question 30

If E = {1, 2, 3, 4, 5, 6, 7, 8, 9}, the subset of E satisfying 5 + x > 10 is

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