class 10 set hint

EX 1.1 7:02 AM

Tuesday, June 22, 2021

Important formulas

Important key word find the by drawing
out of, total ,survey =
either or =
as well as and both =
Neither nor ,antonym
we fill the Venn diagram from=

book page 5
Q 2a if n(A) =35 and n(B) =30 and
venn diagram

Solution
n(A) =35
n(B) =30

from venn diagram

3a) if P={ multiples of 2 up to 20} , Q={ multiples of 3 up to 24} and U= {integers

from 1 to 25} find by drawing venn diagram

solution

P={2,4,6,8,10,12,14,16,18,20}

Q={3,6,9,12,15,18,21,24}

U { , ,3, , ,6,7,8,9, , , , 3,… }

Q4) in a set A and B A has 40 members and 50 members and
6 By how many element
for made ?

solution

n(A)= 40
n(B)=50

set Page 1

n(B)=50
6

we have ,

6
69

Q 5a) if n(A)=40 , n(B) =60 and 8 find the value of draw a
venn diagram .

n(A)= 40 8
n(B)=60

we have ,

Q 6) if A and B are two sub sets of universal set U in which n(U) =70 n(A) =40 ,

n(B)=20 and then show it in a Venn diagram find the value of

solution
n(U) =70
n(A) =40 ,
n(B)=20

From the venn diagram
76

Q 7a) In a survey of 60 people , 30 drinks mil , 25 drink curd and 10 students drink
milk as well as curd , draw Venn diagram find the students who drink neither of them

solution
Let M and C denote the set of students who drink Milk and curd respectively
n(U)= 60

set Page 2

n(M) = 30
n( C ) =25

Q 8 b) In a survey before an election 65% people liked leader A and 60% people liked
leader B .If 15 % people did not like to open their opinion of any of the leader find the
percentage of people who liked both the leader by using Venn diagram

Solution :
Let A denote the set of people who like the leader A and B denotes the set of people
who like the leader B

n(A)=65
n(B)=60

from the Venn diagram
n(U) =

Q 9 a) In a group of 100 students, 68 like football game and 60 like Volleyball game . By
drawing a Venn diagram find
i) How many students like both games?
ii) How many students like only football?
iii) Show the above information on Venn diagram

solution
Let F and V denotes the sets of students who like the football or Volleyball
respectively
n(U)= 100
n(F)=68
n(F)=60
from the Venn diagram

68 6

Q10 a) out of 90 civil servant , 65 were working in the office ,50 were working in
the field and 35 were working in both the premises
i) how many civil servant were absent ?
ii) How many civil servant were working in the field only?
iii) Represent the above information in the Venn diagram ?
Solution

set Page 3

Solution
Let O and F denotes the set of workers who works in office and field
respectively
n(U)=
n(O)=
n(F)=

we have ,

we have

now representing on the Venn diagram

Q 11 a) In an examination , it was found that 55% failed in math and 45% failed in
English if 35% passed in both subjects
iv) What percentage failed in math only?
v) What percentage failed in English only?
vi) Represent the above the above information in a Venn diagram .
Solution
Let M and E denotes the sets of students who failed in the Math and English
respectively
n(U) =
n(M)=
n( E) =

3

we have
n(U) =

now representing in Venn diagram

Q12a) In an exam ,70% of the examination Passed in Science, 75% in the math and
10% failed in the both subject .If 220 examination passed in both subjects , find
the total number of students

set Page 4

the total number of students

solution
Let S and M denotes
if n(U)=100
n(S)=
n(M)=

from Venn diagram

n(U)= 7 7

55% of total study the both subjects
So,

total students=

Q 13) In a class of 25 students , 12 have chosen Mathematics , 8 have choose
Mathematics but not Biology . If each of them has Chosen at least one, then find
the numbers of students who have chosen Mathematics and Biology and those
who have chosen Biology but not Mathematics solve by making a Venn diagram .
solution :
Let M and B denotes the sets of students wo has chosen the math and
n(U) =25

from Venn diagram
n(U) = 8

Q 14 ) out of 100 students of class V 73 passed in mathematics and 84 in Nepali
in the final examination but 7 failed in both and 5 were absent in the examination .
Find the number of students who passed in the both subjects
solution
Let M and v denotes the sets of students …
n(U) =
n(M)=

set Page 5

n(M)=
n(N) =

7

from the Venn diagram

n(U) = 8 7

Q 15) out of 100 students in a class 20 student like math but not science and 30
students like science but not math . If 20 students kike neither of both subjects
i) Show the above information in a Venn diagram
Ii) find the ratio of the students who like math to the student who like science
solution
Let
n(U) =

from the Venn diagram

n(U) = 3

3
n(M) =

The ration of students who like math to science =

Q15 b) 250 students in a group were asked whether they like mango apple . 80
students like mango but not apple and 60 students like apple but not mango . If 50
students do not like both of fruits then
i) Represent the above information in Venn diagram
ii) Find the ratio of the students who like to the students who like apple

Solution
Let
n(U)=

from Venn diagram
n(U) =

set Page 6

Ex2 ,
Q) 2a) If n(A) = 65 n(B) =50 n( C) = 40 ,

,,

,

solution
we have

n(U) =

Q 2 b) sets A ,B and C are the subjects of the universal set U if n(A)=48 , n(B)=
,n C , …

solution

n(U) =

3a) 3 b) use

4a) 4b) if n(A) =12 n(B)= 12 ,…
same as 2 b
5a)
Use

n(U) =

6a)

in an interview of 45 students , 12liked mathematics and science , 5liked matematic and
english , 25 liked mathemataaics , 23liked sciene , 4 liked all three subjects. 15liked
english , 10 liked and english . How many students did not like any of the subjects ?
Solution , let M,S, Edenote the sets of students who liked the Mathematics , Science, and
English respectively

3

set Page 7

we have ,

7a)

1) Ina vilage of 140 house , 60 believe in buddhiism, 70 in hindudism relion and 45 in other
religion . Among them 17 houses donot find any difference in Hindusim and buddism , 18
houses donot find any difference in hinduism and other religion . 16 houdes donot find
anny diffenence between buddhism and other religion . If 16 houses donot believe in any
religion find how many houses donot find any diffenecce in any religion .show it in venn
diagram
Solution , let B, H, O denote the set of houses which beieve in buddism Hinddudim , other
relogion

6, 7, 6
7, 8

6,

we have,

6

3

then draw Venn diagram
8a)

in a group of students , 20 study Account, 21 study Mathematics , 18 History , 7 study
Account only . 10 study mathememtics only , 6 study account and Mathematics only and 3
student Mathemaics and History only
i) How many students study all the subjects ?
ii) how many students are there altogether ?

Solution
Let A,M, H, denotes the sets of students who likes the account mathematics and history
respectively

set Page 8

respectively 8 6 3
,
,7
From the venn diagram

9a) use n(U)= 100

use
n(U)=

set Page 9