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Test: Relations and Functions- Case Based Type Questions- 1 - JEE MCQ


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10 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Relations and Functions- Case Based Type Questions- 1

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Test: Relations and Functions- Case Based Type Questions- 1 - Question 1

Direction: Read the following text and answer the following questions on the basis of the same:

A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever Let I be the set of all citizens of India who were eligible to exercise their voting right in general election held in 2019. A relation ‘R’ is defined on I as follows:

ONE – NATION

ONE – ELECTION

FESTIVAL OF DEMOCRACY

GENERAL ELECTION - 2019

R = {(V1, V2) : V1, V2 ∈ I and both use their voting right in general election – 2019}

Two neighbours X and Y ∈ I. X exercised his voting right while Y did not cast her vote in general election - 2019. Which of the following is true?

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 1 - Question 1
(X, Y) ∉ R

∵ X exercised his voting right while, Y did not cast her vote in general election-2019

And R = {(V1, V2) : V1 V2 ∈ I and both use their voting right in general election-2019}

Test: Relations and Functions- Case Based Type Questions- 1 - Question 2

Direction: Read the following text and answer the following questions on the basis of the same:

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1, 2, 3, 4, 5, 6}. Let A be the set of players while B be the set of all possible outcomes.

A = {S, D}, B = {1, 2, 3, 4, 5, 6}

Let R : B → B be defined by R = {(1, 1), (1, 2), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}, then R is

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 1 - Question 2

Check Reflexive

Since x is divisible by x

Therefore, (x,x) R

Therefore, R is reflexive.

Check Symmetric

To check whether symmetric or not,

If (x,y) R, then (y,x) R

Here, (2,4) R, as 4 is divisible by 2

But, (4,2) ∉ R as 2 is not divisible by 4

Therefore, R is not Symmetric.

Check Transitive

If y is divisible by x and z is divisible by y,

Then z is divisible by x

Therefore, if (x,y) R & (y,z) R, then (x,z) R

Therefore, R is transitive.

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Test: Relations and Functions- Case Based Type Questions- 1 - Question 3

Direction: Read the following text and answer the following questions on the basis of the same:

A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever Let I be the set of all citizens of India who were eligible to exercise their voting right in general election held in 2019. A relation ‘R’ is defined on I as follows:

ONE – NATION

ONE – ELECTION

FESTIVAL OF DEMOCRACY

GENERAL ELECTION - 2019

R = {(V1, V2) : V1, V2 ∈ I and both use their voting right in general election – 2019}

Mr. ’X’ and his wife ‘W’ both exercised their voting right in general election -2019, Which of the following is true?

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 1 - Question 3
Given R = {(V1, V2 ∈ I and both use their voting rights}

Since X voted, and W also voted.

Therefore, both (X, W) ∈ R and (W, X) ∈ R

Test: Relations and Functions- Case Based Type Questions- 1 - Question 4

Direction: Read the following text and answer the following questions on the basis of the same:

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1, 2, 3, 4, 5, 6}. Let A be the set of players while B be the set of all possible outcomes.

A = {S, D}, B = {1, 2, 3, 4, 5, 6}

Let R be a relation on B defined by R = {(1, 2), (2, 2), (1, 3), (3, 4), (3, 1), (4, 3), (5, 5)}. Then R is

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 1 - Question 4
R = {(1, 2), (2, 2), (1, 3), (3, 4), (3, 1), (4, 3), (5, 5)}

R is not reflexive.

Since, (1, 1), (3, 3), (4, 4), (6, 6) ∈ R

R is not symmetric.

Because, for (1, 2) ∈ R there does not exist (2, 1) ∈ R.

R is not transitive.

Because for all element of B there does not exist, (a, b) (b, c) ∈ R and (a, c) ∈ R.

Test: Relations and Functions- Case Based Type Questions- 1 - Question 5

Direction: Read the following text and answer the following questions on the basis of the same:

A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever Let I be the set of all citizens of India who were eligible to exercise their voting right in general election held in 2019. A relation ‘R’ is defined on I as follows:

ONE – NATION

ONE – ELECTION

FESTIVAL OF DEMOCRACY

GENERAL ELECTION - 2019

R = {(V1, V2) : V1, V2 ∈ I and both use their voting right in general election – 2019}

The above defined relation R is __________

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 1 - Question 5
R is reflexive, since every person is friend or itself.

i.e., (F1, F2) ∈ R

Further, (F1, F2) ∈ R

⇒ F1 is friend of F2

⇒ F2 is friend of F1

⇒ (F2, F1) ∈ R

⇒ R is symmetric

Moreover, (F1, F2), (F2, F3) ∈ R

⇒ F1 is friend of F2 and F2 is friend of F3.

⇒ F1 is a friend of F3.

⇒ (F1, F3) ∈ R

Therefore, R is an equivalence relation.

Test: Relations and Functions- Case Based Type Questions- 1 - Question 6

Direction: Read the following text and answer the following questions on the basis of the same:

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1, 2, 3, 4, 5, 6}. Let A be the set of players while B be the set of all possible outcomes.

A = {S, D}, B = {1, 2, 3, 4, 5, 6}

Let R : B → B be defined by R = {(x, y) : y is divisible by x} is

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 1 - Question 6
R is reflexive, since every element of B i.e.,

B = {1, 2, 3, 4, 5, 6} is divisible by itself.

i.e., (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) ∈ R

further, (1, 2) ∈ R

but (2, 1) ∉ R

Moreover,

(1, 2), (2, 4) ∈ R

⇒ (1, 4) ∈ R

⇒ R is transitive.

Therefore, R is reflexive and transitive but not symmetric.

Test: Relations and Functions- Case Based Type Questions- 1 - Question 7

Direction: Read the following text and answer the following questions on the basis of the same:

A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever Let I be the set of all citizens of India who were eligible to exercise their voting right in general election held in 2019. A relation ‘R’ is defined on I as follows:

ONE – NATION

ONE – ELECTION

FESTIVAL OF DEMOCRACY

GENERAL ELECTION - 2019

R = {(V1, V2) : V1, V2 ∈ I and both use their voting right in general election – 2019}

Mr. Shyam exercised his voting right in General Election - 2019, then Mr. Shyam is related to which of the following?

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 1 - Question 7
Given R = {((V1, V2) : V1, V2 ∈ I and both use their voting rights}

So, Mr. Shyam will be related to all eligible voters who casted their votes.

Test: Relations and Functions- Case Based Type Questions- 1 - Question 8

Direction: Read the following text and answer the following questions on the basis of the same:

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1, 2, 3, 4, 5, 6}. Let A be the set of players while B be the set of all possible outcomes.

A = {S, D}, B = {1, 2, 3, 4, 5, 6}

Raji wants to know the number of relations possible from A to B. How many numbers of relations are possible?

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 1 - Question 8
Given A = {S,D}, B = {1, 2, 3, 4, 5, 6}

Number of relation from A to B

= 2 Numbers of elements of A x Number of elements of B

= 22 x 6

= 212

Test: Relations and Functions- Case Based Type Questions- 1 - Question 9

Direction: Read the following text and answer the following questions on the basis of the same:

A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever Let I be the set of all citizens of India who were eligible to exercise their voting right in general election held in 2019. A relation ‘R’ is defined on I as follows:

ONE – NATION

ONE – ELECTION

FESTIVAL OF DEMOCRACY

GENERAL ELECTION - 2019

R = {(V1, V2) : V1, V2 ∈ I and both use their voting right in general election – 2019}

Three friends F1, F2 and F3 exercised their voting right in general election-2019, then which of the following is true?

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 1 - Question 9
Given R = {((V1, V2) : V1, V2 ∈ I and both use their voting rights}

Since all 3 friends F1, F2 and F3 voted

Therefore, (F1, F2) ∈ R, (F2, F3) ∈ R and (F1, F3) ∈ R

Test: Relations and Functions- Case Based Type Questions- 1 - Question 10

Direction: Read the following text and answer the following questions on the basis of the same:

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1, 2, 3, 4, 5, 6}. Let A be the set of players while B be the set of all possible outcomes.

A = {S, D}, B = {1, 2, 3, 4, 5, 6}

Raji wants to know the number of functions from A to B. How many number of functions are possible?

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 1 - Question 10
Given A = {S,D}, B = {1, 2, 3, 4, 5, 6}

So, A has 2 elements, B has 6 elements

Number of functions from A to B = 6*6

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