Class XII

The range of function f(x) = [x] is :
  1. -------------------------------------------------------------------------------- Q (set of rational No.)
  2. R – Z
  3. Z
  4. R
A function f : X → Y is said to be onto if
  1. No element of Y is the image of some element of X under f
  2. Every element of Y is the image of some element of X under f
  3. every element of Y is the image of same element of X under f
  4. Some elements of Y are the images of some element of X under f
A function f : X → Y f : X → Y is defined to be one – one (or injective), if
  1. the images of distinct elements of X under f are identical
  2. the images of distinct elements of X under f are not distinct
  3. the images of distinct elements of X under f are not defined
  4. the images of distinct elements of X under f are distinct
Let A = {1, 2, 3}. Which of the following is not an equivalence relation on A ?
  1. {(1, 1), (2, 2), (3, 3), (2, 3), (3, 2)}
  2. {(1, 1), (2, 2), (3, 3)}
  3. none of these.
  4. {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}
Let A = {1, 2, 3}, then the domain of the relation R = {(1, 1), (2, 3), (2, 1)} defined on A is
  1. -------------------------------------------------------------------------------- {1, 2}
  2. {1, 3}
  3. none of these
  4. {1, 2, 3}
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