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 IMPORTANT QUESTIONS 11 CLASS MATHEMATICS (NCERT,CBSE,DIRECTOR OF EDUCATION).

                                                                                                                                            

                                                     Chapter-1

                                                           Sets

Specific Questions (4 Mark)

Que 1:-.   

In a survey it was found that 21 people liked product A, 26 liked product B and29 liked product C. If 14 people liked products A and B, 12 people liked productsC and A, 14 people liked products B and C and 8 liked all the three products.

•Find how many liked product C only.

ANSWER:-

Given:-

n(A)=a+b+c+d................(1)

n(B)=b+c+f+g.................(2)

n(C)=c+d+e+f..................(3)

n(A∩B)=b+c=14...............(4)

n(B∩C)=c+f=14...............(5)

n(A∩C)=c+d=12...................(6)

n(A∩B∩C)=c=8...............,..(7)

Now,

Putting value of c in equ. 4

b+c=14

b+8=14

b=6

Again,

Putting value of c in equ. 5

c+f=14

8+f=14

f=6

Again,

Putting value of c in equ. 6

c+d=12 

8+d=12

d=4

Since, According to questions

Putting value of c,d,f in equ. 3

c+d+e+f=29

8+4+e+6=29

e+18=29

e=29-18

e=11

So, No. of liked product C=11

Que.2

In a survey of 60 people, it was found that 25 people read newspaper 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 newspapers. Find:

(i) the number of people who read at least one of the newspapers.

(ii) the number of people who read exactly one newspaper.

Ans:-

Let C be the set of people who read newspaper I.

Given n(A)=25,n(B)=26, and n(C)=26

n(A∩C)=9,n(A∩B)=11, and (B∩C)=8

n(A∩B∩C)=3

Let U be the set of people who took part in the survey.

(i) n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(C∩A)+n(A∩B∩C)

=25+26+26−11−8−9+3

=52

Hence, 52 people read at least one of the newspaper.

(ii) Let a be the number of people who read newspapers H and T only.

Let b denote the number of people who read newspapers I and H only.

Let c denote the number of people who read newspaper T and I only.

Let d denote the number of people who read all three newspaper.

Accordingly, d=n(A∩B∩C)=3

Now, n(A∩B)=a+d

n(B∩C)=c+d

n(C∩A)=b+d

∴a+d+c+d+b+d=11+8+9=28

⇒a+b+c+d=28−2d=28−6=22

Hence, (52−22)=30 people read exactly one newspaper

Que.3

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?

Answer:-

So No. of student were taking neither tea or coffee = 325.

Que.4

In a survey of 400 students in a school, 100 were listed as taking apple

juice, 150 as taking orange juice and 75 were listed as taking both apple as well as

orange juice. Find how many students were taking neither apple juice nor orange juice.

Answer:-

 Que.5

There are 200 individuals with a skin disorder, 120 had been exposed to

the chemical C1, 50 to chemical C2, and 30 to both the chemicals C1and C2. 

Find thenumber of individuals exposed to

(i) Chemical C1but not chemical C2

(ii) Chemical C2but not chemical C1

(iii) Chemical C1or chemical C2

Answer:-

Que 6:-

In a group of 84 persons, each plays at least one game out of 

three viz. tennis, badminton and cricket. 28 of them play cricket, 

40 play tennis and 48 play badminton. If 6 play both cricket and 

badminton and 4 play tennis and badminton and no one plays all 

the three games, find the number of persons who play cricket 

but not tennis.

Answer:- 

Que.7

In a class, 18 students took Physics, 23 students took Chemistry 

and 24 students took Mathematics of these 13 took both 

Chemistry and Mathematics, 12 took both Physics and 

Chemistry and 11 took both Physics and Mathematics. If 6 

students offered all the three subjects, find: 

(1) The total number of students. 

(2) How many took Maths but not Chemistry.

Answer:-

2) n(C-B)= n(C)-n(B∩C)

                  =24 -13

     n(C-B) = 11

                                                                                                                                            

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