NTC EXAMS 2024

NTC Numeracy Past Question And Answer 2023 (Set Of Numbers) 3

BRIGHT FRANCISOctober 20, 2023

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NTC Numeracy Past Question And Answer 2023 (Set Of Numbers)

NTC Literacy Past Question And Answer 2023 ( Conditional Sentences)

NTC Literacy Past Question And Answer 2023 ( Conditional Sentences 2)

NTC Literacy Past Question And Answer 2023 (Subject- Verb agreement) 1

Q.1: How many elements are there in the complement of set A?
A. 0
B. 1
C. All the elements of A
D. None of these
Answer: A. 0
Explanation: The complement of a set A will contain the elements that are not present in set A.

Q.2: Empty set is a _______.
A. Infinite set
B. Finite set
C. Unknown set
D. Universal set
Answer: B. Finite set
Explanation: The cardinality of the empty set is zero, since it has no elements. Hence, the size of the empty set is zero.

Q.3: The number of elements in the Power set P(S) of the set S = {1, 2, 3} is:
A. 4
B. 8
C. 2
D. None of these
Answer: B. 8
Explanation: Number of elements in the set S = 3
Number of elements in the power set of set S = {1,2,3} = 23

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NTC Numeracy Past Question And Answer 2023 (Set Of Numbers)

NTC Literacy Past Question And Answer 2023 ( Conditional Sentences)

NTC Literacy Past Question And Answer 2023 ( Conditional Sentences 2)

NTC Literacy Past Question And Answer 2023 (Subject- Verb agreement) 1

= 8

Q.4: Order of the power set P(A) of a set A of order n is equal to:
A. n
B. 2n
C. 2n
D. n2
Answer: C. 2n
Explanation: The cardinality of the power set is equal to 2n, where n is the number of elements in a given set.

Q.5: Which of the following two sets are equal?
A. A = {1, 2} and B = {1}
B. A = {1, 2} and B = {1, 2, 3}
C. A = {1, 2, 3} and B = {2, 1, 3}
D. A = {1, 2, 4} and B = {1, 2, 3}
Answer: C. A = {1, 2, 3} and B = {2, 1, 3}
Explanation: Two sets are said to be equal if they both have the same elements.

Q.6: Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, P = {1, 2, 5}, Q = {6, 7}. Then P ∩ Q’ is :
A. P
B. Q
C. Q’
D. None
Answer: A. P
Explanation: Given,
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
P = {1, 2, 5}
Q = {6, 7}
Q’ = {1, 2, 3, 4, 5, 8, 9, 10}
Hence,
P ∩ Q’ = {1, 2, 5} = P

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NTC Numeracy Past Question And Answer 2023 (Set Of Numbers)

NTC Literacy Past Question And Answer 2023 ( Conditional Sentences)

NTC Literacy Past Question And Answer 2023 ( Conditional Sentences 2)

NTC Literacy Past Question And Answer 2023 (Subject- Verb agreement) 1

Q.7: The cardinality of the power set of {x: x∈N, x≤10} is ______.
A. 1024
B. 1023
C. 2048
D. 2043
Answer: A. 1024
Explanation: Given,
Set X = {x: x∈N, x≤10}
X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Number of elements of power set of X, P(X) = 210 = 1024

Q.8: Write X = {1, 4, 9, 16, 25,…} in set builder form.
A. X = {x: x is a set of prime numbers}
B. X = {x: x is a set of whole numbers}
C. X = {x: x is a set of natural numbers}
D. X = {x: x is a set of square numbers}
Answer: D. X = {x: x is a set of square numbers}
Explanation: Given,
X = {1, 4, 9, 16, 25,…}
X = {12, 22, 32, 42, 52, …}
Therefore,
X = {x: x is a set of square numbers}

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NTC Numeracy Past Question And Answer 2023 (Set Of Numbers)

NTC Literacy Past Question And Answer 2023 ( Conditional Sentences)

NTC Literacy Past Question And Answer 2023 ( Conditional Sentences 2)

NTC Literacy Past Question And Answer 2023 (Subject- Verb agreement) 1

Q.9: If A, B and C are any three sets, then A × (B ∪ C) is equal to:
A. (A × B) ∪ (A × C)
B. (A ∪ B) × (A ∪ C)
C. (A × B) ∩ (A × C)
D. None of the above
Answer: A. (A × B) ∪ (A × C)
Explanation: Given,
A, B and C are any three sets.
Now, A × (B ∪ C) = (A × B) ∪ (A × C)

Q.10: The range of the function f(x) = 3x – 2‚ is:
A. (- ∞, ∞)
B. R – {3}
C. (- ∞, 0)
D. (0, – ∞)
Answer: A. (- ∞, ∞)
Hint:
Let the given function be
y = 3x – 2
⇒ y + 2 = 3x
⇒ x = (y + 2)/3
Since, for all values of y, x has different values. Thus, values of x and y can range from -∞ to ∞.
So, Range{f(x)} = R = (-∞, ∞).

11. What is the sum of the digits in the two-digit number?
A. 6
B. 12
C. 18
D. 24
Answer: B. 12

12. If the sum of the digits of a two-digit number is 10, and the difference between the digits is 3, what could be the number?
A. 37 or 73
B. 24 or 42
C. 68 or 86
D. 55 or 55
Answer: A. 37 or 73

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NTC Numeracy Past Question And Answer 2023 (Set Of Numbers)

NTC Literacy Past Question And Answer 2023 ( Conditional Sentences)

NTC Literacy Past Question And Answer 2023 ( Conditional Sentences 2)

NTC Literacy Past Question And Answer 2023 (Subject- Verb agreement) 1

13. If the sum of the digits of a two-digit number is 15, and the difference between the digits is 9, what is the number?
A. 69
B. 96
C. 24
D. 51
Answer: B. 96

14. If the sum of the digits of a two-digit number is 8, and the difference between the digits is 4, what are the possible numbers?
A. 26 or 62
B. 35 or 53
C. 47 or 74
D. 59 or 95
Answer: A. 26 or 62

15. If the sum of the digits of a two-digit number is 11, and the difference between the digits is 5, what is the number?
A. 24
B. 86
C. 62
D. 53
Answer: C. 62

16. What is the difference between the digits of a two-digit number if the sum of the digits is 7 and the number is greater than 70?
A. 1
B. 2
C. 3
D. 4
Answer: B. 2

17. If the sum of the digits of a two-digit number is 13, and the difference between the digits is 7, what are the possible numbers?
A. 46 or 64
B. 29 or 92
C. 58 or 85
D. 73 or 37
Answer: A. 46 or 64

18. If the sum of the digits of a two-digit number is 9, and the difference between the digits is 3, what is the number?
A. 63
B. 72
C. 45
D. 54
Answer: B. 72

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NTC Numeracy Past Question And Answer 2023 (Set Of Numbers)

NTC Literacy Past Question And Answer 2023 ( Conditional Sentences)

NTC Literacy Past Question And Answer 2023 ( Conditional Sentences 2)

NTC Literacy Past Question And Answer 2023 (Subject- Verb agreement) 1

19. If the sum of the digits of a two-digit number is 14, and the difference between the digits is 8, what is the number?
A. 51
B. 59
C. 86
D. 95
Answer: D. 95

20. What is the sum of the digits of a two-digit number if the difference between the digits is 1 and the number is less than 50?
A. 5
B. 6
C. 7
D. 8
Answer: C. 7

21. If the sum of the digits of a two-digit number is 16, and the difference between the digits is 6, what are the possible numbers?
A. 37 or 73
B. 89 or 98
C. 24 or 42
D. 51 or 15
Answer: B. 89 or 98

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NTC Numeracy Past Question And Answer 2023 (Set Of Numbers)

NTC Literacy Past Question And Answer 2023 ( Conditional Sentences)

NTC Literacy Past Question And Answer 2023 ( Conditional Sentences 2)

NTC Literacy Past Question And Answer 2023 (Subject- Verb agreement) 1

22. If the sum of the digits of a two-digit number is 6, and the difference between the digits is 2, what is the number?
A. 15
B. 33
C. 42
D. 24
Answer: D. 24

23. If the sum of the digits of a two-digit number is 10, and the difference between the digits is 2, what is the number?
A. 28
B. 37
C. 46
D. 55
Answer: A. 28

24. What is the sum of the digits of a two-digit number if the difference between the digits is 4 and the number is greater than 60?
A. 9
B. 8
C. 7
D. 6
Answer: B. 8

24. If the sum of the digits of a two-digit number is 12, and the difference between the digits is 4, what could be the number?
A. 86 or 68
B. 31 or 13
C. 42 or 24
D. 59 or 95
Answer: A. 86 or 68

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NTC Numeracy Past Question And Answer 2023 (Set Of Numbers)

NTC Literacy Past Question And Answer 2023 ( Conditional Sentences)

NTC Literacy Past Question And Answer 2023 ( Conditional Sentences 2)

NTC Literacy Past Question And Answer 2023 (Subject- Verb agreement) 1

25. What is A × (B ∪ C) equivalent to?
A. (A × B) ∪ (A × C)
B. (A ∪ B) × (A ∪ C)
C. (A × B) ∩ (A × C)
D. None of the above
Answer: A

26. If A = {1, 2}, B = {2, 3}, and C = {3, 4}, what is A × (B ∪ C)?
A. {(1, 2), (1, 3), (1, 4), (2, 2), (2, 3), (2, 4)}
B. {(1, 2), (2, 3), (3, 4)}
C. {(1, 3), (2, 4)}
D. {(1, 1), (2, 2), (3, 3), (4, 4)}
Answer: A

27. What does the Cartesian product A × (B ∪ C) represent in set theory?
A. The intersection of sets A and B ∪ C
B. The union of sets A and B ∪ C
C. The set of all possible ordered pairs where the first element is from set A and the second element is from either B or C.
D. The complement of sets A, B, and C
Answer: C

28. If A = {a, b} and B = {b, c} and C = {c, d}, what is A × (B ∪ C)?
A. {(a, b), (a, c), (a, d), (b, b), (b, c), (b, d)}
B. {(a, b), (b, c), (c, d)}
C. {(a, c), (b, d)}
D. {(a, a), (b, b), (c, c), (d, d)}
Answer: A

29. Which set operation is equivalent to A × (B ∪ C)?
A. A × B ∪ A × C
B. A × (B ∩ C)
C. (A × B) ∩ (A × C)
D. (A ∪ B) × (A ∪ C)
Answer: A

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NTC Numeracy Past Question And Answer 2023 (Set Of Numbers)

NTC Literacy Past Question And Answer 2023 ( Conditional Sentences)

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NTC Literacy Past Question And Answer 2023 (Subject- Verb agreement) 1

30. If A contains n elements, B contains m elements, and C contains p elements, how many elements will be in the set A × (B ∪ C)?
A. n × m + n × p
B. n × (m + p)
C. n × (m + p) × 2
D. n + m + p
Answer: B

31. What is the cardinality of the set A × (B ∪ C) in terms of the cardinalities of A, B, and C?
A. |A × (B ∪ C)| = |A| × |B ∪ C|
B. |A × (B ∪ C)| = |A| + |B ∪ C|
C. |A × (B ∪ C)| = |A| × (|B| + |C|)
D. |A × (B ∪ C)| = |A| × |B| × |C|
Answer: C

32. If A = {1, 2, 3}, B = {3, 4}, and C = {4, 5}, what is A × (B ∪ C)?
A. {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 3), (3, 4), (3, 5)}
B. {(1, 4), (2, 3), (3, 5)}
C. {(1, 3), (2, 4), (3, 5)}
D. {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5)}
Answer: A

33. What is the relationship between A × (B ∪ C) and (A × B) ∪ (A × C)?
A. They are equal.
B. They are disjoint sets.
C. A × (B ∪ C) is a subset of (A × B) ∪ (A × C).
D. (A × B) ∪ (A × C) is a subset of A × (B ∪ C).
Answer: A

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NTC Numeracy Past Question And Answer 2023 (Set Of Numbers)

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NTC Literacy Past Question And Answer 2023 (Subject- Verb agreement) 1

34. If A contains no elements (A = ∅), what is A × (B ∪ C)?
A. ∅
B. A × B ∪ A × C
C. B ∪ C
D. A × (B ∪ C)
Answer: A

35. Given sets A = {p, q, r}, B = {r, s}, and C = {s, t}, what is A × (B ∪ C)?
A. {(p, r), (p, s), (p, t), (q, r), (q, s), (q, t), (r, r), (r, s), (r, t)}
B. {(p, r), (q, s), (r, t)}
C. {(p, s), (q, t)}
D. {(p, p), (q, q), (r, r), (s, s), (t, t)}
Answer: A

36. What is the set operation that represents the set of all possible ordered pairs where the first element is from set A and the second element is from either B or C?
A. A × (B ∪ C)
B. (A × B) ∪ (A × C)
C. (A ∪ B) × (A ∪ C)
D. A × (B ∩ C)
Answer: A

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NTC Numeracy Past Question And Answer 2023 (Set Of Numbers)

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NTC Literacy Past Question And Answer 2023 (Subject- Verb agreement) 1

Mathematics Education:
37. If A represents the set of math textbooks, B represents the set of science textbooks, and C represents the set of literature textbooks in a library, what does A × (B ∪ C) represent?
A. Math and science textbooks
B. Math textbooks borrowed with either science or literature textbooks
C. The intersection of math textbooks and science or literature textbooks
D. None of the above
Answer: B

Market Analysis:
38. In market analysis, A represents the set of customers interested in product A, B represents the set of customers interested in product B, and C represents the set of customers interested in product C. What does A × (B ∪ C) represent in this context?
A. Customers interested in product A or B
B. Customers who have purchased both product A and either product B or C
C. Customers who have purchased product A, and some of them may have purchased either product B or C
D. None of the above
Answer: B

E-commerce:
39. Suppose A represents a set of online shoppers, B represents a set of shoppers who prefer credit card payments, and C represents a set of shoppers who prefer PayPal. What does A × (B ∪ C) represent in the context of an e-commerce platform?
A. Online shoppers who prefer credit card or PayPal payments
B. Online shoppers who have made a purchase using either a credit card or PayPal
C. Online shoppers who have made a purchase using a credit card, and some may have used PayPal
D. None of the above
Answer: B

Academic Courses:
40. In a university’s course offerings, if A represents the set of mathematics courses, B represents the set of computer science courses, and C represents the set of elective courses, what does A × (B ∪ C) represent?
A. Math and computer science courses
B. Math courses combined with either computer science or elective courses
C. The intersection of math courses and computer science or elective courses
D. None of the above
Answer: B

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NTC Numeracy Past Question And Answer 2023 (Set Of Numbers)

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NTC Literacy Past Question And Answer 2023 (Subject- Verb agreement) 1

Inventory Management:
41. In a retail store, if A represents the set of available products, B represents the set of products in high demand, and C represents the set of products on sale, what does A × (B ∪ C) represent in terms of inventory management?
A. Available products that are in high demand or on sale
B. Available products with a potential high demand or sale status
C. Available products that are both in high demand and on sale
D. None of the above
Answer: B

42. Social Media Marketing:
In a social media marketing campaign, if A represents the set of target audience members, B represents the set of users who engage with posts, and C represents the set of users who share posts, what does A × (B ∪ C) represent in terms of campaign reach?
A. Target audience members who engage with posts or share posts
B. Potential reach to target audience members who may engage with posts or share posts
C. Target audience members who both engage with and share posts
D. None of the above
Answer: B

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NTC Numeracy Past Question And Answer 2023 (Set Of Numbers)

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NTC Literacy Past Question And Answer 2023 (Subject- Verb agreement) 1

Transportation Planning:
43. In urban transportation planning, if A represents the set of road networks, B represents the set of bus routes, and C represents the set of subway lines, what does A × (B ∪ C) represent in terms of transit options?
A. Road networks that include both bus routes and subway lines
B. Road networks with potential intersections with bus routes or subway lines
C. Road networks that intersect with either bus routes or subway lines
D. None of the above
Answer: B

44. Library Holdings:
In a university library, if A represents the set of available books, B represents the set of reference books, and C represents the set of periodicals, what does A × (B ∪ C) represent in the context of library holdings?
A. Available books that are reference books or periodicals
B. Available books with potential reference or periodical status
C. Available books that can be categorized as either reference books or periodicals
D. None of the above
Answer: B

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NTC Numeracy Past Question And Answer 2023 (Set Of Numbers)

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NTC Literacy Past Question And Answer 2023 ( Conditional Sentences 2)

NTC Literacy Past Question And Answer 2023 (Subject- Verb agreement) 1

45. Healthcare Services:
In a healthcare network, if A represents the set of medical facilities, B represents the set of primary care services, and C represents the set of specialty services, what does A × (B ∪ C) represent in terms of healthcare offerings?
A. Medical facilities offering both primary care and specialty services
B. Medical facilities that may offer primary care or specialty services
C. Medical facilities providing primary care and having the potential to provide specialty services
D. None of the above
Answer: B

46. Online Education:
In an online education platform, if A represents the set of courses, B represents the set of video lectures, and C represents the set of quizzes, what does A × (B ∪ C) represent in terms of course content?
A. Courses that include both video lectures and quizzes
B. Courses that may include video lectures or quizzes
C. Courses that provide video lectures and have the potential to include quizzes
D. None of the above
Answer: B

47. Customer Support:
In a customer support system, if A represents the set of customer inquiries, B represents the set of phone calls, and C represents the set of email inquiries, what does A × (B ∪ C) represent in terms of communication channels?
A. Customer inquiries received through phone calls or email
B. Customer inquiries that may be received via phone calls or email
C. Customer inquiries that are received via phone calls and may also be received via email
D. None of the above
Answer: B