Math, asked by ayaanmakanimakani, 10 days ago

State T for true' and F for Talse' and select the correct option. 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. Then (0) The numb f students passed in English and Mathematics but not in

Science is 2.

(1) The number of students passed in Mathematics only is 2.

(2) The number of students passed in more than one subject is 9.

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Answers

Answered by hritikk0708
10

Answer:

I HOPE THIS WILL HELP YOU

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Answered by mathdude500
15

\large\underline{\sf{Solution-}}

Given that,

  • 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

Now, using venn diagram [ see in attachment ]

Number of students passed in English = 15

\rm\implies \:a + d + e + g = 15 -  -  - (1) \\

Number of students passed in Mathematics = 12

\rm\implies \:b + e + f + g = 12 -  -  - (2) \\

Number of students passed in Science = 8

\rm\implies \:c + d + f + g = 8 -  -  - (3) \\

Number of students passed in English and Mathematics = 6

\rm\implies \:e + g = 6 -  -  - (4) \\

Number of students passed in Mathematics and Science = 7

\rm\implies \:f + g = 7 -  -  - (5) \\

Number of students passed in English and Science = 4

\rm\implies \:d + g = 4 -  -  - (6) \\

Number of students passed in all 3 subjects = 4

\rm\implies \ g = 4 -  -  - (7) \\

So, Substitute (7) in (6), (7) in (5), (7) in (4)we get

\rm\implies \:d = 0 \\

\rm\implies \:f = 3 \\

\rm\implies \:e = 2 \\

On substituting d, e, f, g in equation (1), (2) and (3), we get

\rm\implies \:a = 9 \\

\rm\implies \:b =3 \\

\rm\implies \:c =1 \\

(0) Number of students passed in English and Mathematics but not in Science = e = 2.

  • So, this statement is True.

(1) Number of students passed in Mathematics only = b = 3

  • So, this statement is False.

(2) Number of students passed in more than one subject = d + e + f + g = 0 + 2 + 3 + 4 = 9.

  • So, this statement is true.

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