Question

100 students of Class XI of a school are assigned roll number 1 to 100. All even Roll

numbered students opted Physics, whose roll numbers are divisible by 3 opted Chemistry

and whose roll numbers are divisible by 5, opted Mathematics.

Based on the above information answer the following.(any four)

18. i Number of students who opted Mathematics

a) 49 b) 50 c) 51 d) 10

1

18. ii Number of students who opted at least one subject.

a) 100 b) 99 c) 74 d) 10

1

18. iii Number of students who opted both Physics and Chemistry

a) 16 b) 99 c) 74 d) 10

1

18. iv Number of students who opted all the three subjects

a) 50 b) 33 c) 20 d) 3

1

18. v Number of students who opted both Mathematics and Chemistry

a) 16 b) 6 c) 26 d) 10​

Answer 1

Given : 100 students of Class XI of a school are assigned roll number 1 to 100.  

All even Roll numbered students opted Physics,

All  Roll numbered divisible by 3 opted Chemistry

All  Roll numbered divisible by 5 opted Mathematics

To Find :

Number of students who opted Mathematics

Number of students who opted at least one subject.

Number of students who opted both Physics and Chemistry

Number of students who opted all the three subjects

Number of students who opted both Mathematics and Chemistry

Solution:

assigned roll number 1 to 100

All even Roll numbered students opted Physics,

2 , 4 , 6 ,..............................., 98 , 100

Students in Physics = 50

All  Roll numbered divisible by 3 opted Chemistry

3 , 6 , 9 ,..............................., 96 , 99

Students in  Chemistry = 33

All  Roll numbered divisible by 5 opted Mathematics

5 , 10 , 15 ,..............................., 95 , 100

Students in  Mathematics = 20

students who opted Mathematics = 20

Number of students who opted all the three subjects

Multiple of 2 , 3 & 5   = 30

three students  roll number  30 , 60 & 90

students who opted both Physics and Chemistry

Multiple of 6   hence 16 students

Number of students who opted both Mathematics and Chemistry

Multiple of 15  hence  6  students

 

Number of students who opted at least one subject.

= Multiiple of 2 + Multiple of 3 +  Multiple of 5  - Multiple of 6 - Multiple of 10

- Multiple of 15  + Multiple of 30

50 + 33 + 20  - 16 - 10 - 6 + 3  = 74

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