1. Which of the following sets is countable?
a) Natural numbers
b) Real numbers
c) Irrational numbers
d) Complex numbers
2. What is the cardinality of the power set of an empty set?
a) 0
b) 1
c) 2
d) Infinite
3. Which of the following operations is NOT closed under the set of real numbers?
a) Addition
b) Subtraction
c) Multiplication
d) Division
4. Given the real number sequence {1, 2, 4, 8, ...}, what is the common ratio?
a) 1/2
b) 2
c) 4
d) 8
5. Which of the following sequences is an arithmetic progression?
a) {1, 3, 5, 7, ...}
b) {2, 4, 8, 16, ...}
c) {1, 2, 4, 7, ...}
d) {1, 1/2, 1/4, 1/8, ...}
6. The sum of the first 10 terms of an arithmetic progression is 155. What is the 20th term if the
common difference is 3?
a) 170
b) 185
c) 200
d) 215
7. In set theory, the complement of a set A with respect to a universal set U is:
a) A ∩ U
b) A ∪ U
c) A'
d) U'
8. How many subsets does a set with n elements have?
a) 2^n
b) 2n
c) n^2
d) n!
9. Which of the following is a transitive property of a relation on a set?
a) Reflexivity
b) Symmetry
c) Antisymmetry
d) Transitivity
10. Given the real number sequence {2, 4, 6, 8, ...}, what is the sum of the first 100 terms?
a) 10,000
b) 10,100
c) 10,200
d) 10,300
11. Which of the following is NOT an operation on real numbers?
a) Addition
b) Subtraction
c) Factorization
d) Division
12. In an arithmetic progression, if the first term is 5 and the common difference is -3, what is the
10th term?
a) -25
b) -22
c) -19
d) -16
13. Which of the following statements about subsets is true?
a) Every set is a subset of itself.
b) The empty set is a subset of every set.
c) Every proper subset is also a subset.
d) All of the above.
14. The sum of an infinite geometric series is 80. If the common ratio is 1/3, what is the first term?
a) 10
b) 20
c) 30
d) 40
15. Which of the following is true for an arithmetic progression with a positive common difference?
a) The terms are always positive.
b) The terms are always negative.
c) The terms alternate between positive and negative.
d) The terms are non-negative.
16. In set theory, the union of two sets A and B is denoted by:
a) A ∩ B
b) A ∪ B
c) A'
d) B'
17. Given the real number sequence {1, 4, 9, 16, ...}, what is the sum of the first 10 terms?
a) 145
b) 165
c) 185
d) 205
18. Which of the following is NOT a property of an arithmetic progression?
a) Common difference
b) Common ratio
c) First term
d) Term position
19. The sum of an arithmetic progression with n terms is given by:
a) (n/2)(first term + last term)
b) (n/2)(2 × first term + (n - 1) × common difference)
c) n × first term
d) n × common difference
20. Which of the following sets is countably infinite?
a) Natural numbers
b) Real numbers
c) Irrational numbers
d) Complex numbers
21. Given the real number sequence {1, 1/2, 1/4, 1/8, ...}, what is the sum of the first 5 terms?
a) 1.875
b) 1.9375
c) 1.96875
d) 1.9921875
22. Which of the following is true for a geometric progression with a common ratio greater than 1?
a) The terms are always positive.
b) The terms are always negative.
c) The terms alternate between positive and negative.
d) The terms are non-negative.
23. In set theory, the intersection of two sets A and B is denoted by:
a) A ∩ B
b) A ∪ B
c) A'
d) B'
24. In an arithmetic progression, if the first term is 3 and the common difference is 2, what is the sum
of the first 15 terms?
a) 120
b) 150
c) 180
d) 210
25. Which of the following is NOT a property of a geometric progression?
a) Common ratio
b) First term
c) Term position
d) Common difference