Set , Relation and function | Part 3 | NDA maths pyq | NDA maths practice question

Straight Lines

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Question no. 31

Let A be the non-void set of the children in a family. The relation ' x is a brother of y ' on A is

looks_one Reflexive

looks_two Symmetric

looks_3 Transitive

looks_4 None of these

Option looks_3 0

very soon 16

Question no. 32

Let A = {1,2,3,4} and let R = { (2,2) , (3,3) , (4,4) , (1,2) } be a relation on A. Then R is

looks_one Reflexive

looks_two Symmetric

looks_3 Transitive

looks_4 None of these

Option looks_two q

ver soon 2

Question no. 33

The void relation on a set A is

looks_one Reflexive

looks_two Symmetric and Transitive

looks_3 Reflexive and Symmetric

looks_4 Reflexive and Transitive

Option looks_3 5: 7

very soon 3

Question no. 34

Let R₁ be arelation defined by R₁ = {(a,b) | a ≥ b , a,b ∊ R }, then

looks_one An equivalence relation on R

looks_two Reflexive , Transitive but not symmetric

looks_3 Symmetric , Transitive but not Reflexive

looks_4 Neither Transitive nor Reflexive but Symmetric

Option looks_4 x-y+101=0

very soon 4

Question no. 35

In order that a relation R defined on a non empty set A is an equivalence relation , it is sufficient , if R

looks_one is reflexive

looks_two is symmetric

looks_3 is transitive

looks_4 possesses all the above three properties

Option looks_two 5

very soon

Question no. 36

Let n(U)= 700 , n(A)= 200 , n(B)= 300 and n(A ∩ B)= 100 , then n(A' ∩ B') =

looks_one 400

looks_two 600

looks_3 300

looks_4 200

Option looks_one 6 sq. unit

very soon 6

Question no. 37

The relation "congruence modulo m " is

looks_one Reflexive only

looks_two Transitive only

looks_3 Symmetric only

looks_4 An equivalence relation

Option looks_two

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Question no. 38

In a town of 10,000 families it was found that 40% family buy newspaper A , 20% buy newspaper B and 10% families buy newspaper C , 5% families buy A and B , 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspaper , then number of families which buy A only is

looks_one 3100

looks_two 3300

looks_3 2900

looks_4 1400

Option looks_two not cross each other

very soon

Question no. 39

Let R and S be two equivalence relations on a set A, then

looks_one R ∪ S is an equivalence relation on A

looks_two R ⊂ S is an equivalence relation on A

looks_3 R - S is an equivalence relation on A

looks_4 None of these

Option looks_3 3

very soon 9

Question no. 40

Let R and S be two relations on a set A , then

looks_one R and S are transitive , then R ∪ S is also transitive

looks_two R and S are transitive , then R ⊂ S is also transitive

looks_3 R and S are reflexive , then R ⊂ S is also reflexive

looks_4 R and S are symmetric , then R ∪ S is also symmetric

Option looks_two 2 sq. unit

very soon 10

Question no. 41

Let L denote the set oa all straight lines in a plane. Let a relation R be defined by α R β ⇔ α ⊥ β , α β ∈ L. Then R is

looks_one Reflexive

looks_two Symmetric

looks_3 Transitive

looks_4 None of these

Option looks_4 x² + a² = b² - y²

very soon 11

Question no. 42

Let R be a relation over the set N N and it is defined by (a,b) R (c,d) ⇒ a + d = b + c . then R is

looks_one Reflexive only

looks_two Symmetric Only

looks_3 Transitive only

looks_4 An equivalence relation

Option looks_4 1/3

very soon 12

Question no. 43

Let n be a fixed positive integer . Define a relation R on the set Z of integers By aRb ⇔ n| a - b |. Then R is

looks_one Reflexive

looks_two Symmetric

looks_3 Transitive

looks_4 Equivalence

Option looks_3 X=2

very son 13

Question no. 44

If the sets A and B are defined as A = {(x,y): y = e^x , x ∈ R }; and B = {(x,y): y = x , x ∈ R }; then

looks_one B ⊆ A

looks_two A ⊆ B

looks_3 A ∩ B = ϕ

looks_4 A ∪ B = A

Option looks_3 Y=-8

very soon14

Question no. 45

If X= { 4ⁿ- 3n - 1 : n ∈ N }; and Y = {9(n-1) : n ∈ N }; then X ∪ Y is equal to

looks_one X

looks_two Y

looks_3 N

looks_4 None of these

Option looks_one never intersect

very soon15

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