#### Sets, Relations and Functions One Mark Questions

11th Standard

Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 25
25 x 1 = 25
1. The number of constant functions from a set containing m elements to a set containing n elements is

(a)

mn

(b)

m

(c)

n

(d)

m+n

2. If the function f:[-3,3]➝S defined by f(x)=x2 is onto, then S is

(a)

[-9,9]

(b)

R

(c)

[-3,3]

(d)

[0,9]

3. The function f:R➝R be defined by f(x)=sinx+cosx is

(a)

an odd function

(b)

neither an odd function nor an even function

(c)

an even function

(d)

both odd function and even function

4. If A⊆B, then A\B is

(a)

B

(b)

A

(c)

Ø

(d)

$\frac{B}{A}$

5. Let R be a relation on the set N given by R={(a,b):a=b-2, b>6}. Then

(a)

(2,4)∈R

(b)

(3,8)∈R

(c)

(6,8)∈R

(d)

(8,7)∈R

6. Let R be the relation over the set of all straight lines in a plane such that l1Rl2 ⇔ l1丄l2 . Then  R is

(a)

symmetric

(b)

reflexive

(c)

transitive

(d)

an equivalent relation

7. Which of the following is not an equivalence relation on z?

(a)

aRb ⇔ a+b is an even integer

(b)

aRb ⇔ a-b is an even integer

(c)

aRb ⇔ a<b

(d)

aRb ⇔ a=b

8. If A = {(x,y) : y = ex, x∈R} and B = {(x,y) : y=e-x, x ∈ R} then n(A∩B) is

(a)

Infinity

(b)

0

(c)

1

(d)

2

9. The relation R defined on a set A= {0,-1, 1, 2} by xRy if |x2+y2| ≤ 2, then which one of the following is true?

(a)

R = {(0,0), (0,-1), (0, 1), (-1, 0), (-1, 1), (1, 2), (1, 0)}

(b)

R-1 = {(0,0), (0,-1), (0, 1), (-1, 0), (1, 0)}

(c)

Domain of R is {0,-1, 1, 2}

(d)

Range of R is {0,-1, 1}

10. Let A and B be subsets of the universal set N, the set of natural numbers. Then A'∪[(A⋂B)∪B'] is

(a)

A

(b)

A'

(c)

B

(d)

N

11. If n((A x B) ∩(A x C)) = 8 and n(B ∩ C) = 2, then n(A) is

(a)

6

(b)

4

(c)

8

(d)

16

12. If two sets A and B have 17 elements in common, then the number of elements common to the set A x B and B x A is

(a)

217

(b)

172

(c)

34

(d)

insufficient data

13. Let R be the universal relation on a set X with more than one element. Then R is

(a)

not reflexive

(b)

not symmetric

(c)

transitive

(d)

none of the above

14. The range of the function ${1\over 1-2sinx}$ is

(a)

$(-∞,-1)\cup\left( {1\over 3},\infty\right)$

(b)

$\left( -1,{1\over 3}\right)$

(c)

$\left[ -1,{1\over 3}\right]$

(d)

$(-∞,-1]\cup [\frac { 1 }{ 3 } ,∞)$

15. The rule f(x) =x2 is a bijection if the domain and the co-domain are given by

(a)

R, R

(b)

R, (0, ∞)

(c)

(0, ∞); R

(d)

[0, ∞); [0,∞)

16. Let X = {a, b,c},y = (1,2,3) then $f:x\rightarrow y$ given by (a, 1) (b, 1) (c, 1) is called:

(a)

onto

(b)

constant function

(c)

one one

(d)

bijective

17. If $f:[-2,2]\rightarrow A$ is given by f(x)=33 then f is onto, if A is:

(a)

[3, 3]

(b)

(3, 3)

(c)

[-24,24]

(d)

(-24, 24)

18. Which one of the following statements is false? The graph of the function $f(x)={1\over x}$

(a)

exist is the first and third quadrant only

(b)

is a reciprocal function

(c)

is defined at x = 0

(d)

it is symmetric about y = x and y = - x.

19. The domain of the function $f(x)=\sqrt{ x - 5 }+ \sqrt{6 - x}$is

(a)

[5, )

(b)

(- , 6)

(c)

[5, 6]

(d)

(-5, ≠6)

20. If f(x) = 1 - x, x ∈ [- 3, 3] then the domain off is

(a)

[- 2,3]

(b)

(- 2,3)

(c)

(- 3, -2)

(d)

[-2, 3)

21. If A = {1,2}, B = {1,3} then n(A x B) =

(a)

2

(b)

4

(c)

8

(d)

0

22. Which one of the following is false?

(a)

A⋂(BΔ\C) = (A ⋂ B)Δ(A ∩ C)

(b)

A∩(B - C) = (A ∩B) \ (A∩C)

(c)

(A U B), = A' ∩ B'

(d)

(A \ B) U B = A ⋂ B

23. Which one of the following is not a singleton set?

(a)

A = {x : 3x - 5 = 0, x ∈ Q}

(b)

B = {| x | = 1 / x ∈ Z}

(c)

{x : x3 - 1 = 0, x ∈ R}

(d)

{x : 30x = 60, x ∈ N}

24. For any four sets A, B, C and D, which of the following is not true?

(a)

A x C   B x D

(b)

(A x B) ∩ (C x D) = (A ∩ C) x (B ∩ D)

(c)

A x (B U,C) = (A x B) U (A x C)

(d)

A x (B ∩ C) = (A x B) ∩ (A x C)

25. If A and B are any two finite sets having m and n elements respectively then the cardinality of the power set of A x B is

(a)

2m

(b)

2n

(c)

mn

(d)

2mn