Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A x B, each having at least three elements is:

  • 219

  • 256

  • 275

  • 275

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2.

If X = {4n - 3n-1 : n ε N} and Y = {9(n-1):n εN}; where N is the set of natural numbers,then X U Y is equal to

  • N

  • Y-X

  • X

  • X

380 Views

3.

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is

  • 256

  • 220

  • 219

  • 219

286 Views

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4.

Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y ⊆ X, Z ⊆ X and Y ∩ Z is empty, is

  • 52

  • 35

  • 25

  • 25


B.

35

Y ⊆ X, Z ⊆ X
Let a ∈ X, then we have following chances that
(1) a ∈ Y, a ∈ Z
(2) a ∉ Y, a ∈ Z
(3) a ∈ Y, a ∉ Z
(4) a ∉ Y, a ∉ Z
We require Y ∩ Z = φ
Hence (2), (3), (4) are chances for ‘a’ to satisfy Y ∩ Z = φ.
∴ Y ∩ Z = φ has 3 chances for a.
Hence for five elements of X, the number of required chance is 
3 × 3 × 3 × 3 × 3 = 35

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5.

Let R be the set of real numbers.
Statement-1 : A = {(x, y) ∈R × R : y - x is an integer} is an equivalence relation on R.
Statement-2 : B = {(x, y) ∈ R × R : x = αy for some rational number α} is an equivalence relation on R.

  • Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. 

  • (2) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1. 

  • Statement-1 is true, Statement-2 is false. 

  • Statement-1 is true, Statement-2 is false. 

171 Views

6.

If A, B and C are three sets such that A ∩ B = A∩ C and A ∪ B = A ∪ C, then

  • A = B

  • A = C

  • B = C

  • B = C

105 Views

7.

A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P (A ∪ B) is 

  • 3/5

  • 0

  • 1

  • 1

177 Views

8.

Let A and B be two events such that straight P space left parenthesis top enclose straight A union straight B end enclose right parenthesis space equals space 1 over 6 comma space straight P space left parenthesis straight A intersection straight B right parenthesis space equals space 1 fourth space and space straight P space left parenthesis top enclose straight A right parenthesis space equals space 1 fourth comma where top enclose straight A stands for complement of event A. Then events A and B are

  • equally likely and mutually exclusive

  • equally likely but not independent

  • independent but not equally likely

  • independent but not equally likely

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9.

Two sets A and B are as under:

A = {(a-b)∈ RxR:|a-5|<1 and |b-5|<1}

B = {(a,b)∈ Rx R: 4(a-6)2 + 9 (b-5)2 ≤ 36},then

  • Neither A ⊂ B nor B ⊂ A

  • B ⊂ A

  • A ⊂ B

  • A ∩ B = ∅


10.

On R, the set of real numbers, a relation p is defined as 'aρb if and only if 1+ ab> 0'. Tnen,

  • ρ is an equivalence relation

  • ρ is reflexive and transitive but not symmetric 

  • ρ is reflexive and symmetric but not transitive 

  • ρ is only symmetric


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