1.
The number of non-empty subsets of the set {1, 2, 3, 4} is
2. If 𝐴 = {1, 2, 3, 4, 5} then the number of proper subsets of A is
3. If A = {2, 3, 4, 8, 10}, B = {3, 4, 5, 10, 12}, C = {4, 5, 6, 12, 14} then (AB)(AC) is equal to
(a) {2, 3, 4, 5, 8, 10, 12} (b) {2, 4, 8, 10, 12}
(c) {3, 8, 10, 12} (d) {2, 8, 10}
4. If 𝐴 ∩ 𝐵 = 𝐵, then
(𝑎) 𝐴 ⊆ 𝐵 (𝑏) 𝐵 ⊆ 𝐴 (𝑐) 𝐴 = 𝜙 (𝑑) 𝐵 = 𝜙
5. For two sets 𝐴 ∪ 𝐵 = 𝐴 if and only if
(𝑎) 𝐵 ⊆ 𝐴 (𝑏) 𝐴 ⊆ 𝐵 (𝑐) 𝐴 ≠ 𝐵 (𝑑) 𝐵 = 𝐴
A
6. The shaded region in the given figure is
C B
(a) A (B C) (b) A (B C) (c) A (B – C) (d) A – (B C)
1 2 3 4 99
7. Express the set 𝐴 = {2 , 3 , 4 , 5 , … , 100} in set builder form
8. How many different set 𝐴 exists such that 𝐴 ∪ {1, 2, 3, 4, 5} = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}?
9. Sets A and B have 3 and 6 elements respectively. What can be the minimum number of
elements in A B
(a) 3 (b) 6 (c) 9 (d) 18
10. If A and B are two sets such that 𝑛(𝐴) = 70, 𝑛(𝐵) = 60 and 𝑛(𝐴 ∪ 𝐵) = 110, then 𝑛(𝐴 ∩ 𝐵) is
equal to
(a) 240 (b) 50 (c) 40 (d) 20
11. Let 𝑛(𝑈) = 700, 𝑛(𝐴) = 200, 𝑛(𝐵) = 300 and 𝑛(𝐴 ∩ 𝐵) = 100 then 𝑛(𝐴𝐶 ∩ 𝐵𝐶 ) =
(a) 400 (b) 600 (c) 300 (d) 200
12. In a town of 10,000 families it was found that 40% family buy newspaper A, 20% buy
newspaper B & 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C
and 4% buy A and C. If 2% families buy all the three newspapers, then number of families
which buy A only is
(a) 3100 (b) 3300 (c) 2900 (d) 1400
13. Let 𝐴 = {4, 5} and 𝑇 = {𝑥|𝑥 = 𝑎1 + 𝑎2 + ⋯ + 𝑎𝑘 , 𝑘 ∈ 𝑁}. Find the number of elements in the set
𝑁 − 𝑇.
14. How many different sets 𝐴 are possible such that 𝐴 ∩ 𝐵 ⊆ 𝐶 ⊆ 𝐴 ∪ 𝐵, where 𝐴 = {1, 2, 3, 4} and
𝐵 = {1, 3, 5, 7}?
15. If 𝑞 is a natural number less than 51, then find the number of values of 𝑞 for which decimal
23
representation of the number 𝑞 is non – terminating repeating decimal.
Narayana Jaipur HO: B-28, Gopalpura Bypass Road, 10-B Scheme, Near Ridhi Sidhi Circle, Jaipur, Rajasthan 302018
16. Convert the following in fraction
𝑖) 1.2787878 … 𝑖𝑖) 0.0002333333 …
17. How many numbers are there which are less than 300 and coprime to 300.
(Bonus:- How many numbers are there which are less than 210 and coprime to 210)
18. Find the number of subsets of the set {1, 2, 3, 4, 5, 6} such that
i) it has 1 as its element
ii) it has 1 as its element and 2 is not there in the subset
iii) it has only odd elements
Answer key
1. 15 2. 31 3. (a) 4. (b)
𝑛
5. (a) 6. (a) 7. 𝐴 = {𝑥|𝑥 = , 𝑛 ∈ 𝑁, 𝑛 ≤ 99}
𝑛+1
8. 32 9. (b) 10. (d) 11. (c)
12. (b) 13. 7 14. 16 15. 36
211 7
16. 𝑖) 165 𝑖𝑖) 30000
17. 100
18. i) 32 ii) 16 iii) 8
Narayana Jaipur HO: B-28, Gopalpura Bypass Road, 10-B Scheme, Near Ridhi Sidhi Circle, Jaipur, Rajasthan 302018
