Mathematics : Sets, Relations and Functions: Multiple choice questions with answers / choose the correct answer with answers - Maths Book back 1 mark questions and answers with solution for Exercise Problems

CHAPTER: Sets, Relations and Functions

Choose the correct or the most suitable answer.

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

(1) Infinity

(2) 0

(3) 1

(4) 2

*Solution*

2. If A = {(x, y) : y = sin x, x ∈ R} and B = {(x, y) : y = cos x, x ∈ R} then A ∩ B contains

(1) no element

(2) infinitely many elements

(3) only one element

(4) cannot be determined.

3. 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?

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

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

(3) Domain of R is {0,-1, 1, 2}

(4) Range of R is {0,-1, 1}

*Solution*

4. If {(x) = |x – 2| + |x + 2|, *x* ∊ R, then

Ans: 1

*Solution*

5. Let R be the set of all real numbers. Consider the following subsets of the plane R x R:

S = {(x, y) : y = x + 1 and 0 < x < 2} and T = {(x, y) : x - y is an integer }

Then which of the following is true?

(1) T is an equivalence relation but S is not an equivalence relation.

(2) Neither S nor T is an equivalence relation

(3) Both S and T are equivalence relation

(4) S is an equivalence relation but T is not an equivalence relation.

*Solution*

6. Let A and B be subsets of the universal set N, the set of natural numbers. Then A’∪ [(A∩B)∪B’] is

(1) A

(2) A’

(3) B

(4) N

*Solution*

7. The number of students who take both the subjects Mathematics and Chemistry is 70. This

represents 10% of the enrollment in Mathematics and 14% of the enrollment in Chemistry. The

number of students take at least one of these two subjects, is

(1) 1120

(2) 1130

(3) 1100

(4) insufficient data

*Solution*

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

(1) 6

(2) 4

(3) 8

(4) 16

*Solution*

9. If *n*(A) = 2 and *n*(B ∪C) = 3, then n[(A x B) ∪ (A xC)] is

(1) 23

(2) 32

(3) 6

(4) 5

*Solution*

10. 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

(1) 217

(2) 172

(3) 34

(4) insufficient data

*Solution*

11. For non-empty sets A and B, if A ⊂ B then (A x B) ∩ (B x A) is equal to

(1) A ∩ B

(2) A x A

(3) B x B

(4) none of these.

*Solution*

12. The number of relations on a set containing 3 elements is

(1) 9

(2) 81

(3) 512

(4) 1024

*Solution*

Let S = {*a,b,c*}

*n*(S) = 3

*n*(S x S) = 9

Number of relations in n{P(SxS)} = 29 = 512

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

(1) not reflexive

(2) not symmetric

(3) transitive

(4) none of the above

*Solution*

Let X ={*a,b,c*}

Then R = Universal relation

= {(a,a), (a,b)(a,c)(b,a), (b,b)(b,c)(c,a), (c,b)(c,c)}

14. Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4), (4, 1)}. Then

R is

(1) reflexive

(2) symmetric

(3) transitive

(4) equivalence

*Solution*

15. The range of the function 1 / 1-2 sin x is

Ans: 4

*Solution*

16. The range of the function *f*(*x*) = |└ *x*┘- *x*| , *x* ∊ R is

(1) [0, 1]

(2) [0, ∞)

(3) [0, 1)

(4) (0, 1)

*Solution*

17. The rule *f*(*x*) = *x*2 is a bijection if the domain and the co-domain are given by

(1) R,R

(2) R, (0, ∞)

(3) (0, ∞),R

(4) [0, ∞), [0, ∞)

*Solution*

18. The number of constant functions from a set containing *m* elements to a set containing *n* elements

is

(1) *mn*

(2) *m*

(3) *n*

(4) *m* + *n*

19. The function *f* : [0, 2π] → [-1, 1] defined by *f*(*x*) = sin *x* is

(1) one-to-one

(2) onto

(3) bijection

(4) cannot be defined

*Solution*

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

(1) [-9, 9]

(2) R

(3) [-3, 3]

(4) [0, 9]

*Solution*

21. Let X = {1, 2, 3, 4}, Y = {a, b, c, d} and *f* = {(1, a), (4, b), (2, c), (3, d), (2, d)}. Then f is

(1) an one-to-one function

(2) an onto function

(3) a function which is not one-to-one

(4) not a function

*Solution*

22. The inverse of

Ans: 1

*Solution*

23. Let *f* : R → R be defined by *f*(*x*) = 1 - |x|. Then the range of *f* is

(1) R

(2) (1,∞)

(3) (-1, ∞)

(4) (-∞, 1]

*Solution*

24. The function f : R → R is defined by *f*(*x*) = sin *x* + cos *x* is

(1) an odd function

(2) neither an odd function nor an even function

(3) an even function

(4) both odd function and even function.

*Solution*

25. The function f : R → R is defined by

is

(1) an odd function

(2) neither an odd function nor an even function

(3) an even function

(4) both odd function and even function.

*Solution*

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11th Mathematics : UNIT 1 : Sets, Relations and Functions : Exercise 1.5: Choose the correct or the most suitable answer | Sets, Relations and Functions | Mathematics

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