**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

- {0, -1}
- {0, 1}
- {-1, 1}
- {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

- 4
- 7
- 6
- 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

- 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

- Reflexive
- Symmetric
- Anti symmetric
- Transitive

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

^{n}P_{2}- 2
^{n}- 2 - 2
^{n}- 1 - none

**Q. 6.** If a function defined by f(x) = x^{2} - 4x + 5 is a bijection, then B =

- R

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

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

- 4
- 2
- 16
- 1

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

- (f+g) (x)
- (fg) (x)
- (f-g) (x)
- fog (x)

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

- A
- P(A)
- none

**Q. 11.**

- 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?

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