9. In a class of 90 students, 60 students play volleyball, 53 students play badminton and 35 students play both of the games. Find the number of students (i) who do not play any one of the two games (ii) who play badminton only, but not volleyball (iii) who play volleyball only, but not badminton (iv)who play at least one of two games? Advance Math Class 10 - Exercise: 1.1

In a class of 90 students, 60 students play volleyball, 53 students play badminton and 35 students play both of the games. Find the number of students (i) who do not play any one of the two games (ii) who play badminton only, but not volleyball (iii) who play volleyball only, but not badminton (iv)who play at least one of two games?

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Solution:

Let the set students play volleyball be V and

The set of students play badminton be B and set of universal be U

Given, 

n(U)= 90

n(V)= 60

n(B)= 53

n(VꓵB)= 35

Therefore,

             = 60 + 53 – 35

             = 78

(i) number of students who do not play any one of the two games,

=n(U)-n(VUB)

= 90 – 78

= 12

(ii) the number of students who play badminton only, but not volleyball,

n(B – V)= n(B) - n(VꓵB)

              = 53 – 35

              = 18

(iii) the number of students who play volleyball only, but not badminton,

n(V – B)= n(V) - n(VꓵB)

              = 60 – 35

              = 25

(iv) the number of students who play at least one of two games,

n(VUB)= n(V) + n(B) - n(VꓵB)

             = 60 + 53 – 35

             = 78

  Exercise: 1.1  

1. For the set A= { x : x Є N and x < 10} and ф, find the followings

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5. In a class test in mathematics and English, it was found that 55 students have passed in Mathematics, 46 have passed in English and 35 passed in both the subjects. If the number of students who appeared in the test is 100, the find

6. In a survey of 550 students in a school, it was found that 175 students drink milk, 300 students drink tea and 110 students drink both milk and tea. Find the number of students who drinks neither milk nor tea.

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8. In a club of 250 members, it is found that 130 of them drink tea and 85 of them drink tea but not coffee. If each of the members of the club drinks at least one of the items between tea and coffee, the find-

9. In a class of 90 students, 60 students play volleyball, 53 students play badminton and 35 students play both of the games. Find the number of students

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