1.In a town of 10,000 families, it was found that 40%
families buy newspaper A,
20% families buy newspaper B and 10% families buy n
ewspaper 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
papers. Find the no. of families which buy
(i) A only (ii) B only (iii) none of A, B, and C.
2.
Two finite sets have m and n elements. The to tal no. of subsets of the first set is 56 more than the total no. of subsets of second set . Find the value of m and n.
3.In a survey of 100 students, the no. of students studying the various languages were found to be English only 18, English but not H indi 23, English and Sanskrit 8, English 26, Sanskrit 48, Sanskrit and Hindi 8, n o language 24. Find
(i) How many students were studying Hindi?
(ii) How many students were studying English and Hi ndi?
4. In a class of 50 students, 30 students like Hindi, 25 like science and 16 like both. Find the no. of students who like
(i) Either Hindi or science
(ii) Neither Hindi nor science.
5.In a class of 25 students, 12 have taken mathematic s, 8 have taken mathematics but not biology. Find the no. of students who have take n both mathematics and biology and the no. of those who have taken biology but not mathematics each student has taken either mathematics or biology or both.
6. These are 20 students in a chemistry class and 30 s tudents in a physics class. Find the number of students which are either in physics class or chemistry class in the following cases.
(i) Two classes meet at the same hour
(ii) The two classes met at different hours and ten students are enrolled in both the courses.
7. In a survey of 25 students, it was found tha t 15 had taken mathematics, 12had taken physics and 11 had taken chemistry, 5 had taken mat hematics and chemistry, 9 had taken mathematics and physics, 4 had taken physics and chemistry and 3 had taken all three subjects. Find the no. of students that had taken
(i) only chemistry
(ii) only mathematics
(iii) onl y physics
(iv) physics and chemistry but mathematics (v) ma thematics and physics but not chemistry
(vi) only one of the subjects
(vii) at le ast one of three subjects
(viii) None of three subjects.
8.A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only thr ee men got medal in all the three sports, how many received medals in exactly t wo of the three sports?
9. In a survey of 60 people, it was found that 25 peop le read news paper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspa per. Find
(i) The no. of people who read at least one of the newspapers.
(ii) The no. of people who read exactly one news pa per.
10.In a survey of 400 students in a school, 100 were list e d as taking apple juice, 150 as taking orange juice and 75 were listed as taking bo th apple as well as orange juice. Find how many students were taking neither apple ju ice nor orange juice.
11. A survey shows that 73% of the India ns like apple s , wherea s 65% like orange s . What % Indians like both apples and oranges?
12. In a school there are 20 teachers who teach mathematics or phys ics. Of these 12 teach mathematics and 4 teach both physics and math ematics. How many teach physics?
13. There are 2 00 individuals with a skin disorder, 120 had been e xposed to the chemical C 1 , 50 to chemical C 2 , and 30 to both the chemicals C 1 and C 2 . Find the number of individuals exposed to
(1) chemical C 1 but not chemical C 2
(2) chemical C 2 but not chemical C 1
(4) chemical C 1 or chemical C 2
14. In a survey it was found that 21 peoples liked prod uct A, 26 like d product B and 29 liked product C. If 14 people liked products A and B, 12 people like C and A, 14 people like B and C and 8 liked all the three produ cts. Find now many liked product C only.
2.
Two finite sets have m and n elements. The to tal no. of subsets of the first set is 56 more than the total no. of subsets of second set . Find the value of m and n.
3.In a survey of 100 students, the no. of students studying the various languages were found to be English only 18, English but not H indi 23, English and Sanskrit 8, English 26, Sanskrit 48, Sanskrit and Hindi 8, n o language 24. Find
(i) How many students were studying Hindi?
(ii) How many students were studying English and Hi ndi?
4. In a class of 50 students, 30 students like Hindi, 25 like science and 16 like both. Find the no. of students who like
(i) Either Hindi or science
(ii) Neither Hindi nor science.
5.In a class of 25 students, 12 have taken mathematic s, 8 have taken mathematics but not biology. Find the no. of students who have take n both mathematics and biology and the no. of those who have taken biology but not mathematics each student has taken either mathematics or biology or both.
6. These are 20 students in a chemistry class and 30 s tudents in a physics class. Find the number of students which are either in physics class or chemistry class in the following cases.
(i) Two classes meet at the same hour
(ii) The two classes met at different hours and ten students are enrolled in both the courses.
7. In a survey of 25 students, it was found tha t 15 had taken mathematics, 12had taken physics and 11 had taken chemistry, 5 had taken mat hematics and chemistry, 9 had taken mathematics and physics, 4 had taken physics and chemistry and 3 had taken all three subjects. Find the no. of students that had taken
(i) only chemistry
(ii) only mathematics
(iii) onl y physics
(iv) physics and chemistry but mathematics (v) ma thematics and physics but not chemistry
(vi) only one of the subjects
(vii) at le ast one of three subjects
(viii) None of three subjects.
8.A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only thr ee men got medal in all the three sports, how many received medals in exactly t wo of the three sports?
9. In a survey of 60 people, it was found that 25 peop le read news paper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspa per. Find
(i) The no. of people who read at least one of the newspapers.
(ii) The no. of people who read exactly one news pa per.
10.In a survey of 400 students in a school, 100 were list e d as taking apple juice, 150 as taking orange juice and 75 were listed as taking bo th apple as well as orange juice. Find how many students were taking neither apple ju ice nor orange juice.
11. A survey shows that 73% of the India ns like apple s , wherea s 65% like orange s . What % Indians like both apples and oranges?
12. In a school there are 20 teachers who teach mathematics or phys ics. Of these 12 teach mathematics and 4 teach both physics and math ematics. How many teach physics?
13. There are 2 00 individuals with a skin disorder, 120 had been e xposed to the chemical C 1 , 50 to chemical C 2 , and 30 to both the chemicals C 1 and C 2 . Find the number of individuals exposed to
(1) chemical C 1 but not chemical C 2
(2) chemical C 2 but not chemical C 1
(4) chemical C 1 or chemical C 2
14. In a survey it was found that 21 peoples liked prod uct A, 26 like d product B and 29 liked product C. If 14 people liked products A and B, 12 people like C and A, 14 people like B and C and 8 liked all the three produ cts. Find now many liked product C only.
