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Sets and Functions MCQs — Mathematics (page 2)

155 multiple-choice questions on Sets and Functions from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.

26. Which pair of sets is disjoint?

  1. 1, 2, 3, 3, 4, 5
  2. a, b, b, c
  3. 1, 3, 5, 2, 4, 6
  4. 2, 4, 1, 2, 3, 4

Answer: C) 1, 3, 5, 2, 4, 6

Explanation: Disjoint sets have no element in common: A cap B = varnothing. SLO M-09-A-11 · Application

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27. A music playlist has 52 songs: 24 are qawwalis, 20 are pop songs and 5 are tagged as both. How many songs are neither qawwali nor pop?

  1. 13
  2. 39
  3. 19
  4. 34

Answer: A) 13

Explanation: At least one = 24 + 20 - 5 = 39; first group only = 19; second group only = 15; exactly one = 34; neither = 52 - 39 = 13. So the answer is 13. SLO M-09-A-14 · Application

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28. Find the next term of the pattern 1, 3, 6, 10, 15, ldots

  1. 20
  2. 18
  3. 21
  4. 25

Answer: C) 21

Explanation: Triangular numbers: add 2, 3, 4, 5, then 6: 15 + 6 = 21. SLO M-09-A-10 · Understanding

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29. The domain of the relation R = (1, 2), (2, 4), (3, 6) is:

  1. 1, 2, 3
  2. 1, 2
  3. 1, 2, 2, 3, 4, 6
  4. 2, 4, 6

Answer: A) 1, 2, 3

Explanation: The domain is the set of first elements of the ordered pairs. SLO M-09-A-15 · Knowledge

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30. Which table shows the relation y = x - 3?

  1. x: 4, 5, 6 to y: 7, 8, 9
  2. x: 4, 5, 6 to y: 1, 1, 1
  3. x: 4, 5, 6 to y: 1, 2, 3
  4. x: 4, 5, 6 to y: 12, 15, 18

Answer: C) x: 4, 5, 6 to y: 1, 2, 3

Explanation: Subtract 3 from each x. SLO M-09-A-16 · Application

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31. Which set is always equal to (A cup B)'?

  1. A' cup B
  2. A' cup B'
  3. A' cap B'
  4. A cap B

Answer: C) A' cap B'

Explanation: (A cup B)' = A' cap B' — the De Morgan's law. SLO M-09-A-13 · Application

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32. In a town survey of 34 people, 16 speak Urdu at home, 13 speak Punjabi at home and 8 speak both. How many people speak neither language at home?

  1. 8
  2. 21
  3. 5
  4. 13

Answer: D) 13

Explanation: At least one = 16 + 13 - 8 = 21; first group only = 8; second group only = 5; exactly one = 13; neither = 34 - 21 = 13. So the answer is 13. SLO M-09-A-14 · Application

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33. In Pascal's triangle the numbers in row 5 (1, 5, 10, 10, 5, 1) add up to:

  1. 25
  2. 64
  3. 32
  4. 30

Answer: C) 32

Explanation: The sum of row n is 2^n, and 2^5 = 32. SLO M-09-A-10 · Understanding

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34. Using the pattern 1 = 1^2, 1 + 3 = 2^2, 1 + 3 + 5 = 3^2, ldots, find the sum of the first 12 odd numbers.

  1. 168
  2. 144
  3. 23
  4. 156

Answer: B) 144

Explanation: The sum of the first n odd numbers is n^2, so the answer is 12^2 = 144. SLO M-09-A-10 · Understanding

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35. n(A) = 40, n(B) = 32 and n(A cap B) = 15. Find n(A cup B).

  1. 25
  2. 72
  3. 87
  4. 57

Answer: D) 57

Explanation: n(A cup B) = n(A) + n(B) - n(A cap B) = 40 + 32 - 15 = 57. SLO M-09-A-12 · Understanding

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36. If A subseteq B, then A cap B =

  1. B
  2. varnothing
  3. A cup B
  4. A

Answer: D) A

Explanation: Every element of A is already in B, so the common part is A itself. SLO M-09-A-11 · Application

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37. The point (-3, 4) lies in quadrant:

  1. III
  2. II
  3. I
  4. IV

Answer: B) II

Explanation: Quadrant I: (+, +); II: (-, +); III: (-, -); IV: (+, -). SLO M-09-A-16 · Application

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38. If (x + 1, 3) = (4, y - 2), then:

  1. x = 4, y = 3
  2. x = 3, y = 5
  3. x = 3, y = 1
  4. x = 5, y = 1

Answer: B) x = 3, y = 5

Explanation: Equal ordered pairs have equal first and equal second elements: x + 1 = 4 Rightarrow x = 3 and y - 2 = 3 Rightarrow y = 5. SLO M-09-A-15 · Knowledge

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39. Which of these shows a relationship between two quantities?

  1. The number 260
  2. The set 1, 2, 3
  3. The cost of petrol is Rs. 260 times the number of litres
  4. A list of names

Answer: C) The cost of petrol is Rs. 260 times the number of litres

Explanation: A relationship links two changing quantities, here C = 260L. SLO M-09-A-10 · Understanding

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40. In a survey of 200 families: 90 read Jang, 80 read Dawn, 70 read Express; 30 read Jang and Dawn, 25 read Dawn and Express, 20 read Jang and Express, and 10 read all three. How many read only Jang?

  1. 80
  2. 50
  3. 40
  4. 60

Answer: B) 50

Explanation: Only Jang = 90 - 30 - 20 + 10 = 50 (the triple overlap was subtracted twice, so add it back once). SLO M-09-A-14 · Application

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41. In a survey of 60 families: 28 read Jang, 25 read Dawn, 20 read Express; 10 read Jang and Dawn, 8 read Dawn and Express, 6 read Jang and Express, and 3 read all three. How many read none of them?

  1. 9
  2. 52
  3. 8
  4. 11

Answer: C) 8

Explanation: At least one = 28 + 25 + 20 - 10 - 8 - 6 + 3 = 52, so none = 60 - 52 = 8. SLO M-09-A-14 · Application

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42. If A = 2, 5, 6, 7, 9, B = 1, 2, 4, 5, 9 and C = 2, 7, 10, 11, find A cap (B cup C).

  1. 2, 7
  2. 1, 2, 4, 7, 10, 11
  3. 2, 5, 7, 9
  4. 6

Answer: C) 2, 5, 7, 9

Explanation: Work out the brackets first. A cap (B cup C) = 2, 5, 7, 9. SLO M-09-A-11 · Application

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43. In a survey of 200 families: 90 read Jang, 80 read Dawn, 70 read Express; 30 read Jang and Dawn, 25 read Dawn and Express, 20 read Jang and Express, and 10 read all three. How many read none of them?

  1. 25
  2. 26
  3. 175
  4. 35

Answer: A) 25

Explanation: At least one = 90 + 80 + 70 - 30 - 25 - 20 + 10 = 175, so none = 200 - 175 = 25. SLO M-09-A-14 · Application

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44. The point (-1, -6) lies in quadrant:

  1. I
  2. II
  3. IV
  4. III

Answer: D) III

Explanation: Quadrant I: (+, +); II: (-, +); III: (-, -); IV: (+, -). SLO M-09-A-16 · Application

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45. The table shows a relation. x 1 2 3 4 --------------- y 3 5 7 9 Which rule fits it?

  1. y = 2x + 1
  2. y = 2x - 1
  3. y = 3x
  4. y = x + 2

Answer: A) y = 2x + 1

Explanation: Check every column: 2(1) + 1 = 3, 2(2) + 1 = 5, 2(3) + 1 = 7, 2(4) + 1 = 9. SLO M-09-A-16 · Application

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46. In a survey of 46 shoppers at a mall, 22 bought clothes, 24 bought shoes and 10 bought both. How many shoppers bought clothes only?

  1. 26
  2. 36
  3. 12
  4. 10

Answer: C) 12

Explanation: At least one = 22 + 24 - 10 = 36; first group only = 12; second group only = 14; exactly one = 26; neither = 46 - 36 = 10. So the answer is 12. SLO M-09-A-14 · Application

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47. Squares are made in a row from matchsticks: 1 square needs 4 sticks, 2 squares need 7, 3 squares need 10. How many sticks are needed for 15 squares?

  1. 49
  2. 60
  3. 45
  4. 46

Answer: D) 46

Explanation: Each new square adds 3 sticks: sticks = 3n + 1 = 3(15) + 1 = 46. SLO M-09-A-10 · Understanding

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48. Out of 39 patients, 17 have fever, 27 have a cough and 9 have both. How many patients are in at least one of the two groups?

  1. 4
  2. 35
  3. 8
  4. 26

Answer: B) 35

Explanation: At least one = 17 + 27 - 9 = 35; first group only = 8; second group only = 18; exactly one = 26; neither = 39 - 35 = 4. So the answer is 35. SLO M-09-A-14 · Application

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49. If A = 1, 2, 3, 4, 5, B = 2, 6, 8, 9, 11 and C = 4, 8, 11, 12, find A - (B cup C).

  1. varnothing
  2. 4, 6, 8, 9, 11, 12
  3. 1, 3, 5
  4. 8, 11, 12

Answer: C) 1, 3, 5

Explanation: Work out the brackets first. A - (B cup C) = 1, 3, 5. SLO M-09-A-11 · Application

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50. If A = 1, 2, then A A =

  1. (1, 1), (1, 2), (2, 1), (2, 2)
  2. 1, 2, 4
  3. (1, 1), (2, 2)
  4. (1, 2), (2, 1)

Answer: A) (1, 1), (1, 2), (2, 1), (2, 2)

Explanation: Pair every element with every element, including itself. SLO M-09-A-15 · Knowledge

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