Test: Set Notations


10 Questions MCQ Test Mathematics For JEE | Test: Set Notations


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Attempt Test: Set Notations | 10 questions in 10 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics For JEE for JEE Exam | Download free PDF with solutions
QUESTION: 1

The set {x: x is an odd number between 10 and 18}:

Solution:

Odd numbers between 10 and 18 are 11, 13, 15, 17 so these all terms will be a part of the required set i.e., {11, 13, 15, 17}

QUESTION: 2

From the sets given below, select equal sets:
A = { 2, 4, 8, 12}
B = {1, 2, 3, 4}
C = {4, 8, 12, 14}
D = {3, 1, 4, 2}

Solution:
  • The sets are equal if they have the exact same elements in them irrespective of the order of elements.
  • Since options, B & D have the exact same number of elements in them. So they are equal sets. 
QUESTION: 3

Which of the following is a set?

Solution:

(a) The collection of all months of a year is a well-defined collection of objects because one can definitely identify a month that belongs to this collection. Hence, this collection is a set.

(b) A collection of novels is not a well-defined collection because one cannot identify a book that belongs to this collection. Hence, this collection is not a set.

(c) A collection of top rich persons can not be defined. Hence, this collection is not a set.

(d) The collection of the ten most talented writers of India is not a well-defined collection because the criteria for determining a writer's talent may vary from person to person. Hence, this collection is not a set.

QUESTION: 4

If Q = {x : x = 1 / y, where y ∈ N}, then:

Solution:

As y ∈ N, y can be 1, 2, 3, 4...
∴ x will be 1, 1/2, 1/3, 1/4...
1 ∈ Q

QUESTION: 5

Write A = {1, 4, 9, 16, 25} in set builder form.

Solution:
  • We know that, 12 = 1, 22 = 4, 32 = 9, 42 = 16, 52 = 25
  • Therefore the set A = {1, 4, 9, 16, 25...} can be written in set builder form as: 
    A = {x: x is the square of a natural number}
QUESTION: 6

A = { x : x ≠ x } represents:

Solution:
  • According to this, x should be a number which is not equal to the number itself and there is no number which is not equal to the number itself.
  • Therefore A is an empty set.
QUESTION: 7

If A = {3, 6, 9, 12} and B = {6, 8, 9} then intersection of A and B is:

Solution:
  • An intersection is the collection of all the elements that are common to all the sets under consideration.
  • Here element 6 & 9 are common in both the sets. So option C is correct. 
QUESTION: 8

Which of the following is a finite set?

Solution:
  • finite set is a set that has a finite number of elements.
  • Since  x2 – 25 = 0 has finite number of elements. So it is a finite set. 
QUESTION: 9

Identify the null set from the following:

Solution:

Since none of the odd number is divisible by 2, so it would be a null set.

QUESTION: 10

Which of the following has only one subset?

Solution:
  • Every set has the empty set as a subset. So if a set has 1 element, like {0}, then it will have 2 subsets: itself and the empty set, which is denoted by { }.
  • So, if a set has only one subset, then this set must be the empty set.
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