CBSE Important Questions class XII mathematics 2008 2

Q. 1. Let f:R -> Range of f given by f(x)= (x+1)² - 1 and The set S = {x: f(x) = f ^-1(x)} is

1. {0, -1}
2. {0, 1}
3. {-1, 1}
4. {1, 1}.

Q. 2. The minimum number of elements that must be added to the relation R = { (1,2), (2,3) } on the set of natural numbers so that it is an equivalence is

1. 4
2. 7
3. 6
4. 5

Q. 3. Let ‘R’ be a reflexive relation on a finite set ‘A’ having ‘n’ elements and let there be ‘m’ ordered pairs in ‘R’. Then

1. 
2. 
3. 
4. none of these.

Q. 4. Let ‘X’ be a family of sets and ‘R’ be a relation defined by ‘A is disjoint from B’ .Then R is

1. Reflexive
2. Symmetric
3. Anti symmetric
4. Transitive

Q. 5. The number of surjections from A = {1, 2, 3, ….. n} on to B = {a, b} is

1. ⁿP₂
2. 2ⁿ - 2
3. 2ⁿ - 1
4. none

Q. 6. If a function defined by f(x) = x² - 4x + 5 is a bijection, then B =

1. R
2. 
3. 
4. 

Q. 7. Let be two functions given by f(x) = 2x - 3, g (x) = x³ + 5. fog^-1(x) is equal to

1. 
2. 
3. 
4. 

Q . 8. If A = { a, b} then the number of binary operations that can be defined on A is

1. 4
2. 2
3. 16
4. 1

Q. 9. Let f(x) = [x] and g(x) = x - [x] then which of the following function is the zero function

1. (f+g) (x)
2. (fg) (x)
3. (f-g) (x)
4. fog (x)

Q. 10. Let ‘A’ be a nonempty set and be a binary operator on defined by Identity element of the operator * is

1. 
2. A
3. P(A)
4. none

Q. 11.

1. 
2. 
3. 
4. none

Q. 12. Let f : R --> R be the signum function. g: R -> R g(x) = [x]. fog and gof coincides on [0, 1]. True/False?