### Class XII

If the mappings f: A → →B and g: B → →C are both bijective, then the mapping A→ →C is
1. -------------------------------------------------------------------------------- one – one but not onto
2. one – one and onto
3. onto but not one – one
4. neither one – one nor onto
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
If A = { 1, 2, 3}, then the relation R = {(1, 2), (2, 3), (1, 3)} in A is
1. -------------------------------------------------------------------------------- symmetric and transitive only
2. symmetric only
3. transitive only
4. reflexive only
The range of the function f(x) = [sin x] is
1. -------------------------------------------------------------------------------- { – 1, 0, 1}
2. {–1, 1}
3. (–1, 1)
4. [1, 1].
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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