Maths : Set Language : Book Back, Exercise, Example Numerical Question with Answers, Solution : Exercise 1.6: Application on Cardinality of Sets

**Exercise 1.6**

**1. (i) If n(A) = 25, n(B)
= 40, n(A**

**(ii) If n(A) = 300, n(A**

**2. If U = { x : x **

**3. Verify n (A **

**(i) A **

**(ii) A
**

**4. In a class, all students take part
in either music or drama or both. 25 students take part in music, 30 students take
part in drama and 8 students take part in both music and drama. Find**

**(i) The number of students who take part
in only music.**

**(ii) The number of students who take
part in only drama.**

**(iii) The total number of students in
the class.**

**5. In a party of 45 people, each one
likes tea or coffee or both. 35 people like tea and**** ****20 people like coffee. Find the number
of people who**

**(i) like both tea and coffee. (ii) do
not like Tea. (iii) do not like coffee.**

**6. In an examination 50% of the students
passed in Mathematics and 70% of students passed in Science while 10% students failed
in both subjects. 300 students passed in both the subjects. Find the total number
of students who appeared in the examination, if they took examination in only two
subjects.**

**7. A **

**8. Out of 500 car owners investigated,
400 owned car A and 200 owned car B, 50 owned both A and B
cars. Is this data correct?**

**9. In a colony, 275 families buy Tamil
newspaper, 150 families buy English newspaper, 45 families buy Hindi newspaper,
125 families buy Tamil and English newspapers, 17 families buy English and Hindi
newspapers, 5 families buy Tamil and Hindi newspapers and 3 families buy all the
three newspapers. If each family buy atleast one of these newspapers then find**

**(i) Number of families buy only one newspaper**

**(ii) Number of families buy atleast two
newspapers**

**(iii) Total number of families in the
colony.**

**10. A survey of 1000 farmers found that
600 grew paddy, 350 grew ragi, 280 grew corn, 120 grew paddy and ragi, 100 grew
ragi and corn, 80 grew paddy and corn. If each farmer grew atleast any one of the
above three, then find the number of farmers who grew all the three.**

**11. In the adjacent diagram, if n( U)
= 125 , y is two times of x and z is 10 more than x, then
find the value of x ,y and z.**

**12. Each student in a class of 35 plays
atleast one game among chess, carrom and table tennis. 22 play chess, 21 play carrom,
15 play table tennis, 10 play chess and table tennis, 8 play carrom and table tennis
and 6 play all the three games. Find the number of students who play (i) chess and
carrom but not table tennis (ii) only chess (iii) only carrom (Hint: Use Venn diagram)**

**13. In a class of 50 students, each one
come to school by bus or by bicycle or on foot. 25 by bus, 20 by bicycle, 30 on
foot and 10 students by all the three. Now how many students come to school exactly
by two modes of transport?**

Tags : Numerical Problems with Answers, Solution | Set Language | Maths , 9th Maths : UNIT 1 : Set Language

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9th Maths : UNIT 1 : Set Language : Exercise 1.6: Application on Cardinality of Sets | Numerical Problems with Answers, Solution | Set Language | Maths

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