Class XII

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
For any two non-empty sets X,Y a function f : X → Y is said to be bijective, if f is
  1. Injective only
  2. Surjective only
  3. Neither one-one nor onto
  4. Both one – one and onto.
A relation R on a non – empty set A is an equivalence relation iff it is
  1. symmetric and transitive
  2. reflexive, symmetric and transitive
  3. Reflexive ,antisymmetric,transitive
  4. reflexive
If N is the set of integers f : N → N, given by f(x) = 2x is --------------------------------------------------------------------------------
  1. -------------------------------------------------------------------------------- one – one but not onto
  2. one – one and onto
  3. Onto
  4. many-one onto
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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