Chapter -01 sets . multiple choice questions. Prakash.
01. The roster form of the set {x: x ∈ N and x 2 + 5x + 6 = 0} is.
a) {−2, −3} b) {2, 3} c) {−2, 3} d) {2 , −3}
02. which of the following is an empty set
a) {x: x ∈ N and (x − 1)(x − 2) = 0} b) {x: x ∈ N and 2x − 1 = 0}
2
c) {x: x ∈ N and x = 4} d) {x: x ∈ N and x is odd}
03. The set builder form of given set 𝐴 = {3, 6, 9, 12} and 𝐵 = {1, 4, 9, … ,100} is
a) 𝐴 = {𝑥 ∶ 𝑥 = 3𝑛, 𝑛 ∈ 𝑁 and 1 ≤ 𝑛 ≤ 5}, 𝐵 = {𝑥 ∶ 𝑥 = 𝑛2 , 𝑛 ∈ 𝑁 and 1 ≤ 𝑛 ≤ 10}
b) 𝐴 = {𝑥 ∶ 𝑥 = 3𝑛, 𝑛 ∈ 𝑁 and 1 ≤ 𝑛 ≤ 4}, 𝐵 = {𝑥 ∶ 𝑥 = 𝑛2 , 𝑛 ∈ 𝑁 and 1 ≤ 𝑛 ≤ 10}
c) 𝐴 = {𝑥 ∶ 𝑥 = 3𝑛, 𝑛 ∈ 𝑁 and 1 ≤ 𝑛 ≤ 4}, 𝐵 = {𝑥 ∶ 𝑥 = 𝑛2 , 𝑛 ∈ 𝑁 and 1 < 𝑛 < 10}
d) none of these
05. The number of subsets if 𝐴 = ∅ is
a) 0 b) 1 c) 2 d) none of these
06. The set of all natural numbers ‘𝑥’ such that 4𝑥 + 9 < 30 is equal to
a) {2, 3, 4, 5} b) {1, 2,3, 4, 5} c) {1, 2,3, 4, 5, 6} d) none of these
07. Which of the following is not a null set?
a) Set of odd natural numbers divisible by 2
b) Set of even prime numbers
c) {𝑥 ∶ 𝑥 is a natural number, 𝑥 < 5 and 𝑥 > 7}
d) {𝑦 ∶ 𝑦 is a point common to any two parallel lines}
08. Which of the following sets is a finite set?
a) 𝐴 = {𝑥 ∶ 𝑥 ∈ 𝑍 and 𝑥 2 − 5𝑥 + 6 = 0} b) 𝐵 = {𝑥 ∶ 𝑥 ∈ 𝑍 and 𝑥 2 is even}
c) 𝐷 = {𝑥 ∶ 𝑥 ∈ 𝑍 and 𝑥 > −10} d) all of these
09. Which of the following is an equal set?
a) 𝐴 = {𝑎, 𝑏, 𝑐, 𝑑}, 𝐵 = {𝑑, 𝑐, 𝑏, 𝑎}
b) 𝐴 = {4, 8, 12, 16}, 𝐵 = {8, 4, 16, 18}
c) 𝐴 = {𝑥 ∶ 𝑥 is a multiple of 10} 𝐵 = {10, 15, 20, 25, 30, … }
d) none of these
10. If 𝐴 = {𝑥 ∶ 𝑥 = 𝑛2 , 𝑛 = 1, 2, 3}, then number of proper subsets is
a) 3 b) 8 c) 7 d) 4
11. Which one of the following have same sense w.r.to open and closed intervals?
a) 𝐴 = [2, 3] and 𝐵 = {𝑥 ∶ 𝑥 ∈ 𝑅, 2 ≤ 𝑥 ≤ 3}
b) 𝐴 = [−3, 5] and 𝐵 = {𝑥 ∶ 𝑥 ∈ 𝑅, −3 < 𝑥 ≤ 5}
c) 𝐴 = [−15, −2] and 𝐵 = {𝑥 ∶ 𝑥 ∈ 𝑅, −15 < 𝑥 < −2}
d) 𝐴 = (−1, 2) and 𝐵 = {𝑥 ∶ 𝑥 ∈ 𝑅, −1 ≤ 𝑥 ≤ 2}
12. if 𝐴 = {𝑥 ∶ 𝑥 ∈ 𝑅, −3 < 𝑥 ≤ 5} then interval form is
a) [−3, 5] b) (-3 , 5] c) [-3 , 5) d) (−3, 5)
13. if 𝐴 = {𝑎, 𝑏, }, 𝐵 = {𝑎, 𝑏, 𝑐, } and A is subset of B then 𝐴 ∪ 𝐵 is
a) 𝐴 b) 𝐵 c) 𝐴 ∩ 𝐵 d) None of these
14. if 𝐴 = {𝑎, 𝑏, }, 𝐵 = {𝑎, 𝑏, 𝑐, } and A is subset of B then 𝐴 ∩ 𝐵 is
a) 𝐴 b) 𝐵 c) 𝐴 ∪ 𝐵 d) None of these
PRAKASH .B , BHADRA P U COLLEGE , DAVANAGERE. 9164186348 BELAKU ACADEMY Page 1
15. The shaded region in the figure represents
a) 𝐴 ∩ 𝐵
b) 𝐴 ∪ 𝐵
c) 𝐵 − 𝐴
d) (𝐴 − 𝐵) ∪ (𝐵 − 𝐴)
16. If 𝐴, 𝐵, 𝐶 are three sets, then 𝐴 ∩ (𝐵 ∪ 𝐶) =
a) (𝐴 ∪ 𝐵) ∩ (𝐴 ∪ 𝐶) b) (𝐴 ∩ 𝐵) ∩ (𝐴 ∩ 𝐶)
c) (𝐴 ∩ 𝐵) ∪ (𝐴 ∪ 𝐶) d) (𝐴 ∩ 𝐵) ∪ (𝐴 ∩ 𝐶)
17. If 𝐴 and 𝐵 are two sets, then (𝐴 − 𝐵) ∪ (𝐵 − 𝐴) ∪ (𝐴 ∩ 𝐵) =
a) only 𝐴 b) 𝐴 ∪ 𝐵 c) (𝐴 ∪ 𝐵)′ d) None of these
18. Which one of the following is (𝐴 − 𝐵) ∪ (𝐵 − 𝐴)?
a) (𝐴 ∪ 𝐵) ∪ (𝐴 − 𝐵) b) (𝐴 ∪ 𝐵) ∪ (𝐴 ∩ 𝐵)
c) (𝐴 ∪ 𝐵) − (𝐴 ∩ 𝐵) d) (𝐴 − 𝐵) ∩ (𝐵 − 𝐴)
19. If 𝐴 and 𝐵 be any two sets, then (𝐴 ∪ 𝐵)′ =
a) 𝐴 b) 𝐴′ ∩ 𝐵′ c) 𝜙 d) 𝐴′ ∪ 𝐵′
18. If 𝐴 is any sub set of U, then (𝑈)′ =
a) 𝐴 b) 𝐴′ c) 𝜙 d) ∪
′
20.If 𝐴 is any sub set of U, then 𝐴 ∪ 𝐴 =
a) 𝐴 b) 𝐴′ c) 𝜙 d) ∪
′
21. If 𝐴 is any sub set of U, then 𝐴 ∩ 𝐴 =
a) 𝐴 b) 𝐴′ c) 𝜙 d) ∪
′
22.U is a universal set then 𝜙 =
a) 𝐴 b) 𝐴′ c) 𝜙 d) ∪
23. If 𝑋 and 𝑌 are two sets and 𝑋 denote the complement of 𝑋, then 𝑋 ∩ (𝑋 ∪ 𝑌)′ =
′
a) 𝑋 b) 𝑌 c) 𝜙 d) 𝑋 ∩ 𝑌
24. If 𝐴 and 𝐵 are two sets, then 𝐴 ∩ (𝐴 ∪ 𝐵) =
1) 𝐴 2) 𝐵 3) 𝜙 4) 𝐴 ∩ 𝐵
25. Two finite sets have 𝑚 and 𝑛 elements. The number of subsets of the first set is 112 more than that of
the second set. The values of 𝑚 and 𝑛 are, respectively,
a) 4, 7 b) 7, 4 c) 4, 4 d) 7, 7
PRAKASH .B , BHADRA P U COLLEGE , DAVANAGERE. 9164186348 BELAKU ACADEMY Page 2
