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Weekly Quiz Competition

Question 1
10 / -1

Which of the following is not a set?

A
The collection of all universities in India

B
The collection of all hard working students of a particular school

C
Thecollection of all members of the Lower house of the Parliament of India

D
The collection of all girls of a particular co-educational school

Solution

The collection of all hard working students of a particular school is not well

defined because the criterion for determining a student as hard working may

vary from person to person.

Therefore, this collection is not a set.

Question 2

10 / -1

Use the following information to answer the question.

X = {a: a is the consonant in the word “RAJENDER”}

Y = {a: a is the consonant in the word “RAKESH”}

Z = {a: a is the consonant in the word “SHRUTI”}

W = {a: a is the consonant in the word “SAKSHI”}

Which of the following sets are equivalent?

Y and z

X and Y

X and Z

X ,Y and Z

Solution

X = {a: a is the consonant in the word “RAJENDER”}

⇒ X = {R, J, N, D}

⇒ n (X) = 4

Y = {a: a is the consonant in the word “RAKESH”}

⇒ Y = {R, K, S, H}

⇒ n (Y) = 4

Z = {a: a is the consonant in the word “SHRUTI”}

⇒ Z = {S, H, R, T}

⇒ n (Z) = 4

W = {a: a is the consonant in the word “SAKSHI”}

⇒ W = {S, K, S, H} = {S, K, H}

⇒ n (W) = 3

Two finite sets are called equivalent, if they have the same number of elements.

Therefore, the sets X, Y and Z are equivalent sets.

Question 3
10 / -1

Which of the following collections is not a set?

A
A collection of all Indian doctors

B
A collection of all hill stations in India

C
A collection of all notorious persons in U.P.

D
A collection of all satellites in the Milky Way galaxy

Solution

A collection of all notorious persons in U.P. is not well-defined because the criterion for determining whether a person is notorious or not may vary from person to person.

The correct answer is C.

Why alternative A is wrong:

The collection of all Indian doctors is well-defined because one can definitely find out whether a person belongs to the collection or not.

∴This collection is a set.

Why alternative B is wrong:

The collection of all hill stations in India is well-defined because one can definitely find out whether a place belongs to this collection or not.

∴This collection is a set.

Why alternative D is wrong:

The collection of all satellites in the Milky Way galaxy is well-defined because one can definitely conclude whether a given star belongs to this collection or not.

∴This collection is a set.
Question 4
10 / -1

Which of the following collections is a set?

A
A collection of all brown chairs in a room

B
A collection of all good songs in the 80’s era

C
A collection of five best batsmen in the world

D
A collection of ten most beautiful girls in the world
Solution
A set is a well-defined collection of objects. A collection of all brown chairs in a room is a well-defined collection of objects as one can definitely find out whether a given chair in the room is brown or not.

Therefore, this collection is a set.

The correct answer is A.

Why alternative B is wrong:

The collection of all good songs in the 80’s era is not well-defined because the criterion for determining of a good song may vary from person to person.

Why alternative C is wrong:

The collection of five best batsmen in the world is not well-defined because the criterion for determining a good batsman may vary from person to person.

Why alternative D is wrong:

The collection of ten most beautiful girls in the world is not well-defined because the criterion for determining a girl as beautiful may vary from person to person.
Q5)

Which of the following statements is correct?

A)
The set of vowels in the word RHYTHM is an empty set.

B)
The set of prime numbers is a finite set.

C)
The cardinal number of the set of repeated letters in the word DIVISIBILITY is 6.

D)
The set of first 20 multiplies of 11 is infinite.

52.20% got it right!
Answer:
A
Solution:

Consider the statement given in alternative A

The word RHYTHM has no vowel. Therefore, the required set is empty.

Thus, the statement given in alternative A is correct.
Question 5
10 / -1

Which of the following statements is correct?

A
The set of vowels in the word RHYTHM is an empty set.

B
The set of prime numbers is a finite set.

C
The cardinal number of the set of repeated letters in the word DIVISIBILITY is 6.

D
The set of first 20 multiplies of 11 is infinite.
Solution
Consider the statement given in alternative A

The word RHYTHM has no vowel. Therefore, the required set is empty.

Thus, the statement given in alternative A is correct.

The correct answer is A.
Q6)

Which of the following alternative is correctly matched?

A)

Set builder form

Roster form

{x: x is consonant in the word MATHEMATICS}

{M, T, H, S}

B)

Set builder form

Roster form

{x: x is even and a prime number }

Φ

C)

Set builder form

Roster form

{x: x is odd and a multiple of 2 }

Φ

D)

Set builder form

Roster form

{x: x is a vowel in the word ARITHMETIC }

{A, E, I, R}

46.37% got it right!
Answer:
C
Solution:

We know that multiplies of 2 are even. Therefore, there is no number which is odd and a multiple of 2.

Thus, this set is an empty set denoted by Φ.
Question 6
10 / -1

Which of the following alternative is correctly matched?

A

Set builder form Roster form

{x: x is consonant in the word MATHEMATICS} {M, T, H, S}

B

Set builder form Roster form

{x: x is even and a prime number } Φ

C

Set builder form Roster form

{x: x is odd and a multiple of 2 } Φ

D

Set builder form Roster form

{x: x is a vowel in the word ARITHMETIC } {A, E, I, R}

Solution

We know that multiplies of 2 are even. Therefore, there is no number which is odd and a multiple of 2.

Thus, this set is an empty set denoted by Φ.
Question 7
10 / -1

Use the following information to answer the next question.

Let A = {x: x is divisible by 6 and 0 < x < 96} and B = {x: x is divisible by 9 and 0 < x < 90}.

What is the cardinal number of set A∩B?

A
16

B
12

C
8

D
4

Solution

A = {x: x is divisible by 6 and 0 < x < 96}

∴ A = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90}

B = {x: x is divisible by 9 and 0 < x < 90}

∴B = {9, 18, 27, 36, 45, 54, 63, 72, 81}

A∩B = {18, 36, 54, 72}

∴n (A∩B) = 4

Thus, the cardinal number of the required set is 4.
Question 8
10 / -1

What is the cardinal number of a set defined by {x: x is a prime number and divisible by 7}?

A
0

B
1

C
2

D
infinite

Solution

The given set is {x: x is a prime number and divisible by 7}

The element of this set is {7}

∴ Cardinal number = 1

Thus, the cardinal number of the given set is 1.
Question 9
10 / -1

Which of the following alternatives correctly shows the roster form of the set of whole numbers less than 30 and divisible by 5?

A
{5, 10, 15, 20, 25, 30}

B
{0, 5, 10, 15, 20, 25, 30}

C
{0, 5, 10, 15, 20, 25}

D
{5, 10, 15, 20, 25}

Solution

The whole numbers less than 30, which are divisible by 5 are 0, 5, 10, 15, 20, 25

Thus, the required set is {0, 5, 10, 15, 20, 25}
Question 10
10 / -1

Which of the following is not an empty set?

W = {x: x is a prime number, 7 < x < 10}
X = {x: x² = −10, x is a real number}
Y = {x: x < 1, x > 4}
Z = {x: x² = 4, x is a natural number}

A
W

B
X

C
Y

D
Z

Solution

A set which does not contain any element is called an empty set.

W = {x: x is a prime number, 7 < x < 10}

There is no prime number lying between 7 and 10.

Therefore, W is an empty set.

X = {x: x² = −10, x is a real number}

There is no real number whose square is negative.

Therefore, X is an empty set.

Y = {x: x < 1, x > 4}

There is no number which is less than 1 and greater than 4.

Therefore, Y is an empty set.

Z = {x: x² = 4, x is a natural number}

It is observed that 2 ∈ N and 2² = 4

∴Z = {2}

Therefore, Z is not an empty set.

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Set builder form	Roster form
{x: x is consonant in the word MATHEMATICS}	{M, T, H, S}

Set builder form	Roster form
{x: x is even and a prime number }	Φ

Set builder form	Roster form
{x: x is odd and a multiple of 2 }	Φ

Set builder form	Roster form
{x: x is a vowel in the word ARITHMETIC }	{A, E, I, R}

Set builder form	Roster form
{x: x is consonant in the word MATHEMATICS}	{M, T, H, S}

Sets - 1

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Sets - 1

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SHARING IS CARING

Question 1

The collection of all universities in India

The collection of all hard working students of a particular school

Thecollection of all members of the Lower house of the Parliament of India

The collection of all girls of a particular co-educational school

Solution

Question 2

Y and z

X and Y

X and Z

X ,Y and Z

Solution

Question 3

A collection of all Indian doctors

A collection of all hill stations in India

A collection of all notorious persons in U.P.

A collection of all satellites in the Milky Way galaxy

Solution

Question 4

A collection of all brown chairs in a room

A collection of all good songs in the 80’s era

A collection of five best batsmen in the world

A collection of ten most beautiful girls in the world

Solution

Answer:

Solution:

Question 5

The set of vowels in the word RHYTHM is an empty set.

The set of prime numbers is a finite set.

The cardinal number of the set of repeated letters in the word DIVISIBILITY is 6.

The set of first 20 multiplies of 11 is infinite.

Solution

Answer:

Solution:

Question 6

Set builder form Roster form {x: x is consonant in the word MATHEMATICS} {M, T, H, S}

Set builder form Roster form {x: x is even and a prime number } Φ

Set builder form Roster form {x: x is odd and a multiple of 2 } Φ

Set builder form Roster form {x: x is a vowel in the word ARITHMETIC } {A, E, I, R}

Solution

Question 7

16

12

8

4

Solution

Question 8

0

1

2

infinite

Solution

Question 9

{5, 10, 15, 20, 25, 30}

{0, 5, 10, 15, 20, 25, 30}

{0, 5, 10, 15, 20, 25}

{5, 10, 15, 20, 25}

Solution

Question 10

W

X

Y

Z

Solution

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Results Announcement on: coming Monday

Set builder form Roster form

{x: x is consonant in the word MATHEMATICS} {M, T, H, S}

Set builder form Roster form

{x: x is even and a prime number } Φ

Set builder form Roster form

{x: x is odd and a multiple of 2 } Φ

Set builder form Roster form

{x: x is a vowel in the word ARITHMETIC } {A, E, I, R}