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Home » Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed (iii) in Mathematics only (iv) in more than one subject only.
Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed (iii) in Mathematics only (iv) in more than one subject only.
CBSE | Class 11 | Maths | NCERT Exemplar | Sets
Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed (iii) in Mathematics only (iv) in more than one subject only.

Solution:

As per the question,

100 = Total number of students

15 = Number of students who passed in English

12 = Number of students who passed in Mathematics

8 = Number of students who passed in Science

6 = Number of students who passed in English and Mathematics

7 = Number of students who passed in Mathematics and Science

4 = Number of students who passed in English and Science

4 = Number of students who passed in all three

U = Let the total number of students

E = Let the number of students passed in English

M = Let the number of students passed in Mathematics

S = Let the number of students passed in Science

NCERT Exemplar Class 11 Maths Chapter 1-13

n(M \cap S \cap E)=a=4

n(M \cap S)=a+d=7

\Rightarrow 4+d=7

\Rightarrow d=3

n(M \cap E)=a+b=6

\Rightarrow 4+b=6

\Rightarrow \mathrm{b}=2

\mathrm{n}(\mathrm{S} \cap \mathrm{E})=\mathrm{a}+\mathrm{c}=4

\Rightarrow 4+c=4

\Rightarrow \mathrm{c}=0

n(M)=e+d+a+b=12

\Rightarrow e+4+3+2=12

\Rightarrow e+9=12

\Rightarrow \mathrm{e}=3

n(E)=g+c+a+b=15

\Rightarrow g+0+4+2=15

\Rightarrow g+6=15

\Rightarrow \mathrm{g}=9

n(S)=f+c+a+d=8

\Rightarrow f+0+4+3=8

\Rightarrow f+7=8

\Rightarrow f=1

As a result, from the above equations, we have,

(i) e = 3 = Number of students in Mathematics only

(ii) a + b + c + d = 4 + 3 + 2 + 0 = 9 = Number of students in more than one subject only

i

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