Sets Question for Practise

CHAPTER- SETS

Important Questions for SLC

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1. If n(A) = 40, n(B) = 50 / n(A∩B) = 15, find the value of n(A∪B)

2. n(U) = 80, n(P) = 50, n(Q) = 30  / n(P∩Q) = 10. Draw the Venn diagram to illustrate the above

information and find the value of n(P∪Q).

3. If n(A) = 45, n(B) = 65 & n(A∪B) = 85 then

a. Find the value of n(A∩B)

b. Find the value of n0 (B)

c. Show it in venndiagram.

4. A survey conducted shows that 75% like milk and 60% like curd. If they like atleast one of them

then]

a. Show it in a Venn diagram.

b. What percent were there, who like both?

c. What was the percent, who like curd only?

5. In survey of 170 girls it was found that 18 girls can neither dance nor can sing, 96 can dance and

69 can sing. By representing these information in a Venn diagram, find the number of girls who can

both dance and sing.

6. Out of 100 students, 80 passed in science, 71 in Mathematics, 10 failed in both subjects and 7 didn't

appear in an examination. Find the number of students who passed in both subject using venn

diagram.

7. In a survey of 120 students, it was found that 17 drink neither tea nor coffee. 88 drink tea and 26

drink coffee. By drawing Venn-diagram, find out the number of students who drink both tea and

coffee.

8. In a survey of 2400 tourists visited in Nepal, it was found that 1650 liked to visit Bhaktapur, 850 liked

to visit Lalitpur and 150 did not like to visit both places:

a. Represent the above information in a Venn-diagram.

b. How many were there who liked to visit both places?

c. How many were there who liked to visit Bhaktapur only?

9. In a survey of 2000 tourists visited in Nepal, it was found that 1125 liked to visit pokhara, 750 liked

to visit Janakpur and 250 did not like to visit both places.

a. Represent the above information in a venn-diagram

b. How many were there who like to visit both places?

c. How many were there who liked to visit janakpur only ?

10. In a school of 80 students of class X were asked what they would like milk or tea 60 said they would

like tea, 50 said they would like milk and 10 said they would like neither milk nor tea. By drawing

Venn-diagram, find the number of students.

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a. (Who like both tea and milk?)

b. (Who like milk only?)

c. (Who like tea only?)

11. In a survey of group 100 students 55 like to read Muna magazine, 45 like Yuba Manch and 14 do

not like to read either of them, Draw a Venn diagram and give of answer to the following How many

of them like to read

a. Muna magazine only

b. Yuba Manch only.

c. Both of them.

12. In a survey of 60 students, 30 drink milk, 25 drink curd and 10 drink milk as well as curd then

a. Draw a venn -diagram of above information.

b. Find the number of students who drink neither of them.

13.Out of 100 students in a S.L.C. Examination, 80 passed in math, 60 passed in science and 50

passed in both subjects.

a. Draw a Venn diagram to illustrate the above information

b. Find the number of students failed in both subjects.

14. In a class of 25 students, 17 like Volleyball, 15 like Basketball and 10 like both games, Illustrate it

with a Venn-diagram and find the number of students who don't like any of the games

15. In a survey of 200 students 125 liked to admit in science faculty, 100 in humanity faculty and 40 like

to admit either of faculties and the rest were found not to be admitted in both faculties.

a. Show the above information in a venn diagram.

b. Find how many were there who don't like to admit in both faculties.

16. Out of 5000 Japanese who are on Nepal tour, 40% have already toured India 30% have also toured

Pakistan. If 10% of them have toured both the countries by drawing Venn-diagram find the number

of tourists those who have not yet visited both the countries.

17. Out of 1350 candidate 600 passed in Health, 700 in social, 350 in Nepali and 50 did not passed in

all three subjects. If 200 passed in Health and social, 150 in Health and Nepali, 100 in social and

Nepali.

a. How many candidates passed in all subjects?

b. Illustrate the above information in a Venn-diagram.

18.G, S & K represent the people who read Gorkhapatra, Samacharpatra & the Kantipur daily. If

n(G∪S∪K) = 100%, n(G) = 50%, n(S) = 55% n(K) = 35%, n(G∩S) = 15, n(S∩K) = 10%, n(G∩K) =

20%, then what percentage of the people read all these three daily papers?

19. Of the total candidates in an examination, 40% students passed in math 45% in science and 55% in

Health. If 10% passed in math and science, 20% in science & Health and 15% in Health and Maths.

a. Draw a Venn-diagram to show the above information

b. Calculate the percentage. Who passed in all three subjects?
                                                     © Dear dipen

CHAPTER- SETS

20. If n(A) = 65, n(B) = 50, n(C) = (A∩B) = 25, n(B∩C) = 20, n(C∩A) = 15, n(A∩B∩C) = 5 and n(U) =

100, find the value of n( A∪ B ∪C )

21. In a survey of 100 people 65 read Kantipur, 45 read Gorkhapatra, 40 read Himalayan times, 25 read

Kantipur as well as Gorkhapatra, 20 read Kantipur as well as Himalayan times, 15 read Gorkhapatra

as well as Himalayan times and 5 read all three news papers.

a. Draw the Venn-diagram to illustrate the above information.

b. How many people don't read all three news papers.

22. In a survey of a group of students it was found that 60 like to listen  poems, 45 liked to listen stories,

35 liked to listen both and 10 did not like to listen both. Then

a. Present the above information in a Venn-diagram.

b. How many students were surveyed?

c. How many students were liked to listen the story only?

23. In a survey of a group showed that 60 liked tea, 45 liked coffee, 30 liked milk, 25 liked coffee as well

as tea. 20 liked tea as well as milk, 15 liked Coffee as well as milk and 10 liked all three how many

were asked this question. Solve by drawing venn -diagram.

24. Among the candidates appeared in an examination, 80% passed in English, 85% in Maths and 75%

in both English and Maths. Find the total number of candidates if 45 candidates were failed in both

English and Maths.

25. By filling the following information in a venn diagram, Find the cardinal number of n (U). n(L) = 14,

n(M) = 13, n(N) = 22, n(L∩M∩N) = 6, n(L∩M) = 7, n(M∩N) = 9, n(L∩N) = 11, n( L ∩ M ∩ N ) = 4

26.In a school 60 students passed in Mathematics, 45 passed in Science and 30 passed in both

subjects.

a. How many students were there in the school?

b. How many students have passed in Mathematics only?

c. How many students had passed in Science only?

d. Represent the above information in a Venn-diagram

27. In a college, 65 are studying in mathematics, 50 students are studying in science and 35 students

are studying in both subjects.

a. How many students are studying in the college?

b. How many students are studying in Mathematics only?

c. How many students are studying in Science only?

d. Represent the above information in a Venn - diagram.

28. In an examination, it was found that 55% failed in Maths and 45% failed English. If there were 35%

passed in both subjects.

a. What percent failed in Maths only?

b. What percent failed in English only?

c. Represent the above information in a venn diagram.Page 3 of                                                        
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29. In a survey of a village, it was found that 85% of the people like Dashain Festival and 60% like Tihar

Festival. If there were 5% people who did not like both festival:

a. What percent liked Dashain Festival only?

b. What percent liked Tihar Festival only?

c. Represent the above information in a Venn-diagram.

30. In a school, all students play either volleyball or football or both. 300 play football. 250 volleyball and

110 play both game draw a Venn diagram to find.

a. Number of students who play football only.

b. Number of students who play volleyball only.

c. The total number of students in the school.

31.In a survey of a community of 240 people, it was found that 151 people could speak Newari

language, 95 could speak English language and 14 could speak neither of the languages.

Represent the above information in a Venn-diagram supposing x as the number of people who can

speak both languages.

a. Find the value of x.

b. Find the number of people who can speak English only.

32. 40% of the students of a school play football, 30% play volleyball and 20% play both. If 90 students

play neither football nor volleyball use Venn-diagram and find the number of students in the school.

Also find the number of students who play only football.

33.Out of 20 staffs in an office, 15 can speak local Newari language other than Nepali language, 8

can speak Bhojpuri, while 3 can not speak any local languages. By drawing venn diagram, find the

number of staffs.

a. Who can speak at least any one local language?

b. Who can speak any one local language only out at the two.

34. 40 students were asked what they would like milk or curd. 30 said they would like curd, 25 said they

would like milk and 5 said they would neither like milk nor curd. By drawing Venn diagram, find the

number of students.

a. Who like milk only?

b. Who like curd only?

c. Who like either milk or curd, any one only?

35. Set P & Q are two subsets of a universal set U. Illustrate the given information in a venn -diagram

& solve the following problems.If n(U) = 40, n(P) = 25, n(Q) = 18, n(P∩Q) = 5 n(P∪Q) = ? n(

= ?, n(P - Q) = ? n(Q-P) = ?

36. If U = {X:X is a positive integer less than 16} A = {Y:Y is a prime number} B = {Z:Z is an odd

number} then write down the cardinal value by drawing venn diagram.

P ∪Q

a. n(A∩B)    

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b. n( A∪ B )

c. n(A - B)      

d. n[U-(A∩B)]

37. By asking question in a group, 110 answered TB spread through drugs, 75 said through smoking

and 60 said through food. Among them, 25 said from both drugs and smoking, 10 said from

smoking & food & 10 said from drug and food, while 5 said from all three.

a. How many pedestrians were involved? Solve by drawing Venn-diagram.

b. How many said TB spreads through drugs only?

38. In a group 30 students read Math, 24 read Economic, 22 read Statistics 14 read Math only,8 read

Economics only, 6 read Math and Statistics only, 2 read Math and Economics only and 8 read

neither of them

a. Find the number of students in their group?

b. How many students read Economics and Statistics only?

c. How many students read all three subjects?

d. Show all the information in Venn-diagram.

39. In a class of 25 students, 12 have taken Mathematics, 8 have taken Mathematics but not Biology.

Find the number of students who have taken Mathematics and Biology and those who have taken

Biology but not Mathematics. Solve by making a Venn-diagram.

40. In a interview of 50 people. 15 liked milk but not coffee, 5 liked coffee and milk and 5 did not like

both. How many liked coffee only? Represent all result in venn diagram also.

41. Each of a group of 20 students study at least one of the three subjects Nepali, English and Maths.

All those who study English also study Nepali 3 study all three subjects. 4 students only study

Nepali. 8 students study English. 14 students study Nepali. Draw Venn-diagram to illustrate above

information.

a. How many students study only Nepali and Maths but not English?

b. How many students study only Maths?

c. Show all the information in Venn diagram?

42. Each group of 25 students studies at least one of the three subjects Nepali, English and Maths. All

those who study English also study Nepali, 4 students study all three subjects, 5 students study only

Nepali. 7 students study English and 15 students study Nepali.

a. Draw the venn-diagram to illustrate above information.

b. How many students study Nepali and Math but not a English?

c. How many students study math only?

43. In a group of students 18 read Account, 19 read Maths, 16 read Science. 6 read Account only, 9

read Maths only, 5 read Maths and Account only, 2 read Maths and Science only. By using venndiagram, find the following

a. How many read all subjects?
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CHAPTER- SETS

b. How many read science only?

c. How many read account and science?

d. How many students are there altogether?

44. Out of 50 students in a class like Mathematics or Science or both. Among them 20 like both subjects

and the ratio of Maths and Science is 3:2

a. Find the number of students who like Maths only.

b. Find the number of students who like Science only.

c. Illustrate the above information in a venn diagram.

45. In a class of 75 students, 30 students liked Nepali but not Science and 25 students liked Science

but not Neplai. If 10 students did not like both, how many students liked both subjects and represent

the above information in venn-diagram.

46. In a class of 55 students, 15 students liked maths but not English and 18 students liked English but

not Math. If 5 students did not like both, how many students liked both subjects and represent the

above information in Venn-diagram.

47. In an election 1400 voters did not cast their votes and 400 votes are declared invalid. Two

candidates A and B in the election A defected B by 60 votes. It was found that A secured 2400 of

total rolled votes. Find the number of voters.

48. In a survey among 100 people, 50 liked coffee, 30 liked milk, 40 liked tea, 20 like coffee only, 25

liked tea only, 10 liked tea and coffee and 5 liked tea, coffee and milk all. Using venn-diagram, find

the number of people who liked neither of these.

49. An ice-cream shop sold three type of ice creams A, B & C out of the customers questioned, 470

liked A, 300 liked B, 350 liked C, 130 liked A and B, 120 liked A and C, 70 liked B and C, 50 liked all

three.

a. Draw the venn-diagram to illustrate above information

b. How many liked exactly two types?

50. A survey was done about mobile and telephone facility 200 people had telephone facility, 25 had

both facility 135 people did not have telephone facility and 300 did not have mobile facility?

a. How many participants in the survey?

b. How many had mobile facility only?

51. In a class of 65 students, 10 students liked Maths but not English and 20 students liked English but

not Maths. If 5 students did not like both how many students liked both subjects? Solve by Venndiagram.

52. In a result of first terminal examination of class ten 20% students are passed in all three subjects

46% failed in Maths, 57% failed in English, 42% failed in dance, 35% failed in Maths and English,

25% failed in English and dance, 15% failed in dance and Maths.

a. Draw venn diagram to show above information

b. Find how many percent failed in all three subjects
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53. In a village of 140 house, 60 believe in Buddhism, 70 in Hindu Religion and 45 in other religion.

Among then 17 house don't find any difference in Hindu and Buddhims, 18 house don't find any

different in Hindu and other religion while 16 houses don't find any difference between Buddhism

and other religion. If 6 houses don't believe in any religion, find how many houses do not find any

difference in any religion. Show it in venn-diagram.

54. In a group of players 40 play Volleyball out of which 25 play volleyball only. 10 play football only

and 8 play badminton only 27 play football, 30 play badminton out of which 15 play volleyball and

badminton both. Using venn-diagram find.

a. How many play all three games?

b. How many play two games only?

55. In an interview of 60 people space times, Rajdhani and Himalayan times are liked by 45, 30 and 15

people respectively. If the total number of people who liked only two magazines in 22 and they liked

at least one of the magazines. Find the number of people who liked all the magazines.

56. In an examination 48% failed in science, 39% in account and 33% in History, 12% in science and

Account, 9% in science and History and 13% in Account and History and 3% in all three subjects.

Draw Venn-diagram to represent the given information and find the.

a. Percentage passed in all three subjects.

b. Percentage failed exactly in two subjects.

c. Percentage failed exactly in one subject.

Answers

1. 75

2. 70

3. 25, 40

4. 35%, 25%

5. 13

6. 68

7. 11

8. 250, 1400

9. 125, 625

10. 40, 10, 20

11. 41, 31, 14

12. 15

13. 10

14. 3

15. 15

16. 2000

17. 100

18. 5%

19. 5%

20. 15

21. 5

22. 80, 10

23. 85

24. 450

25. 32

26. 75, 30, 15

27. 80, 30, 15

28. 20%, 10%

29. 35%, 10%

30. 190, 140, 440

31. 20, 75

32. 180, 36

33. 17, 11

34. 5, 10, 15

35. 38, 2, 20, 13

36. 5, 6, 1, 10

37. 205, 80

38. 54, 6, 8

39. 4, 13

40. 25

41. 2, 6

42. 3,10

43. 3, 7, 7, 36

44. 22, 8

45. 10 

46. 17

47. 6540

48. 20

49. 170

50. 335, 10

51. 30

52. 10%

53. 10

54. 10, 12

55. 4

56. 11%, 25%, 61%