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Relations and Functions Test - 5

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Relations and Functions Test - 5
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Weekly Quiz Competition
  • Question 1
    1 / -0
    Which of the following relations is a function?
  • Question 2
    1 / -0

    Let x be any real, then [x + y] = [x] + [y] holds for

    Solution

    [x]=x  ∀ x∈I

    so,

    [x+y]=[x]+[y] only if x and y ∈ I

  • Question 3
    1 / -0
    Let f(x) =  then (fofof) (x) equals to
  • Question 4
    1 / -0

    If f (x) =√−x, then domain of fof is

    Solution

    √f(x)  is defined only if

    f(x)will be non negative.

    Hence ∴√−f(x is defined only for 0.

  • Question 5
    1 / -0
    The range of the function f(x) = -  is equal to
  • Question 6
    1 / -0

    If f(x)=|x|x;x≠0; then f (x) – f (- x)  is equal to

    Solution

    f(x)=|x|/x=x/x=1

    f(−x)=|−x|/−x=x/−x=−1

    f(x)−f(−x)=1−(−1)=1+1=2

  • Question 7
    1 / -0
    The domain of the function f = {(1, 3), (3, 5), (2, 6)} is
  • Question 8
    1 / -0
    Determine the domain of the following relation.

    R = {(a, b):a a < 5, b = 4}
  • Question 9
    1 / -0
    If a set A has n distinct elements, then the number of relations on A is
  • Question 10
    1 / -0
    If f(x) = ex, which of the following is true?
  • Question 11
    1 / -0
    A and B are two sets having 3 and 4 elements respectively and having 2 elements in common. The number of relations, which can be defined from A to B, is
  • Question 12
    1 / -0
    If f(x + y) = f(x) + f(y) and f(1) + f(2) + f(3) + ……. + f(10) = 1, find the value of f(1).
  • Question 13
    1 / -0
    Which of the following functions is an even function?
  • Question 14
    1 / -0
    The range of , where x 0, is
  • Question 15
    1 / -0
    If f(x) = , then f(1994) is
  • Question 16
    1 / -0
    The range of the function  is  
  • Question 17
    1 / -0
    The relation R defined on set A = {1, 2, 3, 4, 5} by R = {(x, y) : |x2 – y2| < 16} is given by
  • Question 18
    1 / -0
    Let A = {1, 2, 3}. The total no. of distinct relations which can be defined over A is
  • Question 19
    1 / -0

    The function f (x) = x + cos x

    Solution

    f(x)=x;g(x)=cosx

    Df=R

    Dg=R

    Df+g=Df∩Dg

    so,

    Df+g=R

    SO given function is defined for all reals

  • Question 20
    1 / -0
    The domain of the real function  –  is
  • Question 21
    1 / -0
    The range of the function f(x) = |x - 1| is
  • Question 22
    1 / -0
    If f(x) = x2 - 3x + 1 and f(2α) = 2f(α), then α is equal to
  • Question 23
    1 / -0
    The diagram given below shows that

  • Question 24
    1 / -0
    The number of relations that can be defined on set A = {a, b, c, d} is
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