Class XII

The range of function f(x) = [x] is :
  1. -------------------------------------------------------------------------------- Q (set of rational No.)
  2. R – Z
  3. Z
  4. R
Which of the following is not an equivalence relation on I, the set of integers ; x, y
  1. -------------------------------------------------------------------------------- x R y x + y is an even integer
  2. x R y x ≤ y
  3. x R y x = y
  4. x R y x – y is an even integer
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 = { 2 , 3 , 6 }. Which of the following relations on A are reflexive ?
  1. -------------------------------------------------------------------------------- R1 = { ( 2,2 ) , ( 3,3 ) , ( 6,6 ) }
  2. R3 = { ( 2,2 ) , ( 3,6 ) , ( 2,6 ) }
  3. none of these
  4. R2 = { ( 2,2 ) , ( 3,3 ) , ( 3,6 ) , ( 6,3 ) }
The function f: N→ →N (N is the set of natural numbers) defined by f(n) = 2n + 3, is
  1. many one onto
  2. injective
  3. surjective
  4. bijective
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