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.
