Page 2 :
Remesh’s mathematics, , Sets – Focus area based questions, , iii) If A and B are two sets such that 𝐴 ⊂ 𝐵, then 𝐴 ∪ 𝐵is, a) A, , b) Null set, , c) B, , (1), d) {𝜙}, , 4. In a survey of 600 students in a school, 150 students were found to be taking tea and 225 students were, taking coffee. 100 were taking both tea and coffee. Find how many students were taking neither tea nor, coffee., , (3), , IMPROVEMENT 2019, 5. a) If the number of proper subsets of a set is 63, then the number of elements of the set is ……….., , (1), , b) If𝐴 = {𝑥: 𝑥 𝑖𝑠 𝑎 𝑙𝑒𝑡𝑡𝑒𝑟 𝑖𝑛 𝑡ℎ𝑒 𝑤𝑜𝑟𝑑 “𝑀𝐴𝑇𝐻𝐸𝑀𝐴𝑇𝐼𝐶𝑆”}and, 𝐵 = {𝑦: 𝑦 𝑖𝑠 𝑎 𝑙𝑒𝑡𝑡𝑒𝑟 𝑖𝑛 𝑡ℎ𝑒 𝑤𝑜𝑟𝑑“𝑆𝑇𝐴𝑇𝐼𝑆𝑇𝐼𝐶𝑆”, then, find, , i) 𝐴 − 𝐵, , (ii) 𝐴 ∩ 𝐵, , (2), , 6. a) In a survey of 600 students in a school 150 students were found to be taking tea and 225 taking coffee,, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee. (2), b) Draw Venn diagrams which represents:, i) (𝐴 ∪ 𝐵)′, , ii) 𝐴′ ∪ 𝐵′, , (2), , MARCH 2019, 7. Let𝐴 = {𝑥: 𝑥𝑖𝑠 𝑎 𝑝𝑟𝑖𝑚𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 11} and, 𝐵 = {𝑥: 𝑥𝑖𝑠𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 2 ≤ 𝑥 ≤ 8}, a) Write 𝐶 = 𝐴 ∩ 𝐵, , (1), , b) Find the number of subsets of C which has 3 elements., , (1), , c) What is the probability of getting a subset of 3 elements from the power set of C?, , (1), , 8. In a school, a survey among400 students, 100 were listed as taking apple juice, 150 as taking, orange juice, and 75 were listed as taking both apple juice as well as orange juice., Teaching Mathematics since 1990, , |[email protected], , 2|P a g e

Page 3 :
Remesh’s mathematics, , Sets – Focus area based questions, , a) How many students take apple juice or orange juice?, , (2), , b) How many take apple juice alone but not orange juice?, , (1), , c) How many students were taking neither apple juice nor orange juice?, , (1), , IMPROVEMENT 2018, 9. a) If 𝐴 = {2,3,4,5}and 𝐵 = {4,5,6,7}, then write:, i), , 𝐴∪𝐵, , ii) 𝐴 ∩ 𝐵, , (2), , b) Which one of the following is equal to {𝑥: 𝑥 ∈ 𝑅, 2 < 𝑥 ≤ 4}?, i) {2,3,4}, , ii) {3,4}, , iii) [2,4], , iv) (2,4], , (1), , 10. Consider the set 𝐴 = {𝑥: 𝑥is an integer, 0 ≤ 𝑥 < 4}, a) Write A in Roster form., , (1), , b) If B = {5,6}, then write 𝐴 × 𝐵., , (1), , c) Write the number of possible relations from A to B., , (1), , 11. a) If U = {1,2,3,4,5,6,7,8,9}; A = {2,4,6,8} , B = {2,3,5,7},, Verify (𝐴 ∪ 𝐵)′ = 𝐴′ ∩ 𝐵′, , (3), , b) If A and B are two disjoint sets with n(A) = 4 and n(B) = 2, then n(A −B) = …………, , (1), , MARCH 2018, 12. a) If 𝐴 = {𝑎, 𝑏, 𝑐}, then write the power set of P(A)., , (1), , b) If the number of subsets with two elements of a set P is 10, then find the total number of elements, in the set P., , (2), , c) Find the number of elements of the power set of P., , (1), , 13. Consider a Venn diagram of the Universal set U = {1,2,3,4,5,6,7,8,9,10,11,12,13}, , Teaching Mathematics since 1990, , |[email protected], , 3|P a g e

Page 5 :
Remesh’s mathematics, , Sets – Focus area based questions, , MARCH 2016, 17. a), , If A is a subset of the set B, then 𝐴 ∩ 𝐵 =. . . . . . . . . . . . . .., , (1), , b) Represent the above set 𝐴 ∩ 𝐵 by Venn diagram., , (2), , c) In a school there are 20 teachers who teach Mathematics or Physics. Of these, 12 teach, Mathematics, 12 teach Physics. How many teach both the subjects?, , (2), , IMPROVEMENT 2015, 18. a) 𝐴 = {𝑥/𝑥, 𝑖𝑠𝑎𝑝𝑟𝑖𝑚𝑒𝑛𝑢𝑚𝑏𝑒𝑟, 𝑥 ≤ 6}., i), , Represent A in roster form., , (1), , ii) Write the power set of A., , (2), , b) Out of 25 members in an office 17 like to take tea, 16 like to take coffee. Assume, that each takes at least one of the two drinks. How many like:, i), , Both coffee and tea?, , (1), , ii) Only tea and not coffee?, , (1), , MARCH 2015, 19. Let 𝐴 = {𝑥: 𝑥 ∈ 𝑊, 𝑥 < 5}and 𝐵 = {𝑥: 𝑥𝑖𝑠𝑎𝑝𝑟𝑖𝑚𝑒𝑛𝑢𝑚𝑏𝑒𝑟𝑙𝑒𝑠𝑠𝑡ℎ𝑎𝑛5}, 𝑈 = {𝑥: 𝑥is an integer, 0 ≤ 𝑥 ≤ 6},, a) Write A, B in roster form., , (1), , b) Find (𝐴 − 𝐵) ∪ (𝐵 − 𝐴), , (2), , c) Verify that (𝐴 ∪ 𝐵)′ = 𝐴′ ∩ 𝐵′, , (2), , IMPROVEMENT 2014, 20. a) If two sets A and B are disjoint, which one among the following is true?, i) 𝐴 ∪ 𝐵 = 𝐴, Teaching Mathematics since 1990, , ii) 𝐴 ∪ 𝐵 = 𝐵, , iii) 𝐴 ∩ 𝐵 = 𝐵, |[email protected], , iv) 𝐴 ∩ 𝐵 = 𝜑, , (1), 5|P a g e