RELATION & FUNCTION MCQ test 1

Q1. A relation f from a set A to a set B is said to be function if every element of set A has one and only one image in set B.

True

False

Q2. The notation f : X →Y means that f is a function from X to Y. X is called the ----- of f .

Domain

Co-domain

Image

None of these

Q3. The notation f : X →Y means that f is a function from X to Y. Y is called the ----- of f .

Domain

Co-domain

Image

None of these

Q4. The image of a function is always a subset of the codomain of the function.

True

False

Q5. Given three relations R, S, T from A = {x, y, z} to B = {u, v, w} defined as:
1) R = {(x, u), (z, v)}
2) S = {(x, u), (y, v), (z, w)}
3) T = {(x, u), (x, v), (z, w)}
Identify which of the given relations is/are function(s) using relations and functions definition.

R is a function from A to B

T is a function from A to B

S is a function from A to B

None of thses

Q6. 'Every function is a relation but every relation is not a function.'

True

False

Q7. If f is a function on real numbers defined as

find f(6).

3

5

7

0

Q8.The domain values are equal to the range values for an ---------function.

Constant

identity

Polynomial

None of these

Q9. If f(x) = x3 – (1/x3), then f(x) + f(1/x) is equal to

2x3

2/x3

0

1

Q10. If f(x) = x2 + 2, x ∈ R, then the range of f(x) is

[2, ∞)

(-∞, 2]

(2, ∞)

(-∞, 2) U (2, ∞)

<

Q11. Which method is adopted for relation between two non empty set.

Set Builder form

Roaster from

Arrow diagram

All of above

Q12. If n(A)=3,n(B)=4. What will be value of n(AXAXB)

12

36

48

None of these

Q13. If n(A)=m , n(B)=n What will be non empty relation between set A to set B.

(2^mn)

(2^mn) +1

(2^mn)X 1

(2^mn) - 1

Q14. If R= {(x, y): x,y∈W,X^2+Y^2=25} Find range of R

{3,4}

{0,3,4,5}

{0,5}

None of these

Q15. Given A= {1,3,5} and B= {2,4} .List the element of R:A →B={(x, y): x,y∈AXB and x>y}

{(3, 2),(5, 2),(5, 4)}

{(3, 4),(1, 4)}

(3, 4),(5, 4)

None of these

Q16.Let R be the relation from Set A to Set b then

R ⊆ AXB

R U AXB

R ∩ AXB

None of these

Q17. If R is relation of a finite set having n elements then number of relation on A is

2^2

2^n^2

2n

(2^n)-1

Q18. Let A= {1, 2, 3,….,14}. Define a relation on a set A by R= {(x, y): 3x – y = 0, where x, y ∈ A}. Which one is the range of relation.

{3, 6, 9}

{3, 6, 9, 12}

{3, 6, 12}

None of these

Q19. Let A = {x, y, z} and B = {a, b}. Find the total number of relations from A into B.

6

64

12

None of these

Q20. If A = {1, 2, 3}, B = {4, 5, 6}, which of the following are relations from A to B? Give reasons in support of your answer.
(i) {(1, 6), (3, 4), (5, 2)}
(ii) {(1, 5), (2, 6), (3, 4), (3, 6)}
(iii) {(4, 2), (4, 3), (5, 1)}
(iv) A × B

(i) and (ii)

(i) and (iii)

(ii) and (iv)

None of these