Sets, Relations and Functions One Mark Questions

11th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 25
    25 x 1 = 25
  1. The number of constant functions from a set containing m elements to a set containing n elements is

    (a)

    mn

    (b)

    m

    (c)

    n

    (d)

    m+n

  2. If the function f:[-3,3]➝S defined by f(x)=x2 is onto, then S is

    (a)

    [-9,9]

    (b)

    R

    (c)

    [-3,3]

    (d)

    [0,9]

  3. The function f:R➝R be defined by f(x)=sinx+cosx is

    (a)

    an odd function

    (b)

    neither an odd function nor an even function

    (c)

    an even function

    (d)

    both odd function and even function

  4. If A⊆B, then A\B is 

    (a)

    B

    (b)

    A

    (c)

    Ø

    (d)

    \(\frac{B}{A}\)

  5. Let R be a relation on the set N given by R={(a,b):a=b-2, b>6}. Then

    (a)

    (2,4)∈R

    (b)

    (3,8)∈R

    (c)

    (6,8)∈R

    (d)

    (8,7)∈R

  6. Let R be the relation over the set of all straight lines in a plane such that l1Rl2 ⇔ l1丄l2 . Then  R is

    (a)

    symmetric

    (b)

    reflexive

    (c)

    transitive

    (d)

    an equivalent relation

  7. Which of the following is not an equivalence relation on z?

    (a)

    aRb ⇔ a+b is an even integer

    (b)

    aRb ⇔ a-b is an even integer

    (c)

    aRb ⇔ a<b

    (d)

    aRb ⇔ a=b

  8. If A = {(x,y) : y = ex, x∈R} and B = {(x,y) : y=e-x, x ∈ R} then n(A∩B) is

    (a)

    Infinity

    (b)

    0

    (c)

    1

    (d)

    2

  9. The relation R defined on a set A= {0,-1, 1, 2} by xRy if |x2+y2| ≤ 2, then which one of the following is true?

    (a)

    R = {(0,0), (0,-1), (0, 1), (-1, 0), (-1, 1), (1, 2), (1, 0)}

    (b)

    R-1 = {(0,0), (0,-1), (0, 1), (-1, 0), (1, 0)}

    (c)

    Domain of R is {0,-1, 1, 2}

    (d)

    Range of R is {0,-1, 1}

  10. Let A and B be subsets of the universal set N, the set of natural numbers. Then A'∪[(A⋂B)∪B'] is

    (a)

    A

    (b)

    A'

    (c)

    B

    (d)

    N

  11. If n((A x B) ∩(A x C)) = 8 and n(B ∩ C) = 2, then n(A) is

    (a)

    6

    (b)

    4

    (c)

    8

    (d)

    16

  12. If two sets A and B have 17 elements in common, then the number of elements common to the set A x B and B x A is

    (a)

    217

    (b)

    172

    (c)

    34

    (d)

    insufficient data

  13. Let R be the universal relation on a set X with more than one element. Then R is

    (a)

    not reflexive

    (b)

    not symmetric

    (c)

    transitive

    (d)

    none of the above

  14. The range of the function \({1\over 1-2sinx}\) is

    (a)

    \((-∞,-1)\cup\left( {1\over 3},\infty\right)\)

    (b)

    \(\left( -1,{1\over 3}\right)\)

    (c)

    \(\left[ -1,{1\over 3}\right]\)

    (d)

    \((-∞,-1]\cup [\frac { 1 }{ 3 } ,∞)\)

  15. The rule f(x) =x2 is a bijection if the domain and the co-domain are given by

    (a)

    R, R

    (b)

    R, (0, ∞)

    (c)

    (0, ∞); R

    (d)

    [0, ∞); [0,∞)

  16. Let X = {a, b,c},y = (1,2,3) then \(f:x\rightarrow y\) given by (a, 1) (b, 1) (c, 1) is called:

    (a)

    onto

    (b)

    constant function

    (c)

    one one

    (d)

    bijective

  17. If \(f:[-2,2]\rightarrow A\) is given by f(x)=33 then f is onto, if A is:

    (a)

    [3, 3]

    (b)

    (3, 3)

    (c)

    [-24,24]

    (d)

    (-24, 24)

  18. Which one of the following statements is false? The graph of the function \(f(x)={1\over x}\)

    (a)

    exist is the first and third quadrant only

    (b)

    is a reciprocal function

    (c)

    is defined at x = 0

    (d)

    it is symmetric about y = x and y = - x.

  19. The domain of the function \(f(x)=\sqrt{ x - 5 }+ \sqrt{6 - x}\)is 

    (a)

    [5, )

    (b)

    (- , 6)

    (c)

    [5, 6]

    (d)

    (-5, ≠6)

  20. If f(x) = 1 - x, x ∈ [- 3, 3] then the domain off is

    (a)

    [- 2,3]

    (b)

    (- 2,3)

    (c)

    (- 3, -2)

    (d)

    [-2, 3)

  21. If A = {1,2}, B = {1,3} then n(A x B) =

    (a)

    2

    (b)

    4

    (c)

    8

    (d)

    0

  22. Which one of the following is false?

    (a)

    A⋂(BΔ\C) = (A ⋂ B)Δ(A ∩ C)

    (b)

    A∩(B - C) = (A ∩B) \ (A∩C)

    (c)

    (A U B), = A' ∩ B'

    (d)

    (A \ B) U B = A ⋂ B

  23. Which one of the following is not a singleton set?

    (a)

    A = {x : 3x - 5 = 0, x ∈ Q}

    (b)

    B = {| x | = 1 / x ∈ Z}

    (c)

    {x : x3 - 1 = 0, x ∈ R}

    (d)

    {x : 30x = 60, x ∈ N}

  24. For any four sets A, B, C and D, which of the following is not true?

    (a)

    A x C   B x D

    (b)

    (A x B) ∩ (C x D) = (A ∩ C) x (B ∩ D)

    (c)

    A x (B U,C) = (A x B) U (A x C)

    (d)

    A x (B ∩ C) = (A x B) ∩ (A x C)

  25. If A and B are any two finite sets having m and n elements respectively then the cardinality of the power set of A x B is

    (a)

    2m

    (b)

    2n

    (c)

    mn

    (d)

    2mn

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