Class XII

Let A be the set of all 50 students of Class X in a school. Let f : A → N be function defined by f (x) = roll number of the student, f is
  1. one – one and onto
  2. one – one but not onto
  3. Onto
  4. many-one onto
If R is the set of real numbers, Let f : R → R be defined as f (x) = 3x, then f is
  1. one – one onto
  2. one – one but not onto
  3. many – one onto
  4. neither one – one nor onto
R = {(1, 1), (2, 2), (1, 2), (2, 1), (2, 3)} be a relation on A, then R is
  1. -------------------------------------------------------------------------------- Reflexive
  2. anti symmetric
  3. symmetric
  4. not antisymmetric
If R is the set of real numbers, a function f:R→R defined asf (x) = x2 , then f is
  1. f is many – one onto
  2. f is neither one – one nor onto
  3. f is many one – one and onto
  4. f is one – one but not onto
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
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