Please wait...

Relations and Functions Test - 11
Menu grid icon
Result Result point icon
Relations and Functions Test - 11
  • Goals icon

    /

    Score
  • Trophy icon

    -

    Rank
White alarm icon Time Taken: -
Result frame illustration
  • Question 1/10
    1 / -0.25

    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?

    Solutions

    (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}

  • Question 2/10
    1 / -0.25

    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

    Solutions

    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.

  • Question 3/10
    1 / -0.25

    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?

    Solutions

    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

  • Question 4/10
    1 / -0.25

    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

    Solutions

    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.

  • Question 5/10
    1 / -0.25

    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 __________

    Solutions

    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.

  • Question 6/10
    1 / -0.25

    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

    Solutions

    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.

  • Question 7/10
    1 / -0.25

    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?

    Solutions

    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.

  • Question 8/10
    1 / -0.25

    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?

    Solutions

    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

  • Question 9/10
    1 / -0.25

    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?

    Solutions

    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

  • Question 10/10
    1 / -0.25

    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?

    Solutions

    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

Close button icon
User Profile
-

Correct (-)

Wrong (-)

Skipped (-)

  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10
Mockers logo Get latest Exam Updates
& Study Material Alerts!
No, Thanks
Arrow pointer icon
Click on Allow to receive notifications
Notification bell icon ×
Open Now