For the function f(x) = 1x. where [x] denotes the greatest intege

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 Multiple Choice QuestionsMultiple Choice Questions

11.

Let R be a relation defined on the set Z of all integers and xRy, when x + 2y is divisible by 3, then

  • A is not transitive

  • R is symmetric only

  • R is an equivalence relation

  • R is not an equivalence relation


12.

Let f : N  R be such that f(1) = 1 and f(1) + 2f(2) +  3f(3) + ... + nf(n) = n(n+ 1) f(n), for all n   N, n 2, where N is the set of natural numbers and R is the set of real numbers. Then, the value of f(500) is

  • 1000

  • 500

  • 1/500

  • 1/1000


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13.

For the function f(x) = 1x. where [x] denotes the greatest integer less than or equal to x, which of the following statements are true?

  • The domain is - , 

  • The range is 0  - 1  1

  • The domain is - , 0  [1, )

  • The range is 0  1


B.

The range is 0  - 1  1

C.

The domain is - , 0  [1, )

We have, f(x) = 1x

Domain = R - {f(x) = 0}

 x  [0, 1}

 Domain of f(x) = R-(0, 1] = - , 0  [1, )and range of f(x)=-1, 0, 1


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14.

If R be the set of all real numbers and f : R ➔ R is given by f(x) = 3x2 + 1. Then, the set f-1([1, 6]) is

  • - 53, 0, 53

  • - 53,  53

  • - 13, 13

  •  - 53, 53


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15.

Let Xnz = x + iy : z2  1n for all integers n  1. Then, n = 1 Xn is

  • a singleton set

  • not a finite set

  • an empty set

  • a finite set with more than one element


16.

The number of onto functions from the set {1, 2, ... , 11} to the set {1, 2, ... , 10} is

  • 5 × 11!

  • 10!

  • 11!2

  • 10 × 11!


17.

If f(x) = 2100x + 1, g(x) = 3100x + 1,  then the set ofreal numbers x such that f{g(x)} = x is 

  • empty

  • a singleton

  • a finite set with more than one element

  • infinite


18.

For any two sets A and B, A - (A - B) equals

  • B

  • A - B

  • A  B

  • AC  BC


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19.

Three sets A, B, C are such that A = B ∩ C and B = C ∩ A, then

  • A ⊂ B

  • A ⊃ B

  • A ≡ B

  • A ⊂ B'


20.

If A = {x : x2 - 5x + 6 = 0}, B={2, 4}, C = {4, 5}, then A x (B ∩ C) is

  • {(2, 4), (3, 4)}


  • {(4, 2), (4, 3)}

  • {(2, 4), (3, 4), (4, 4)}

  • {(2, 2), (3, 3), (4, 4), (5, 5)}


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