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In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.
The number of students who had taken only physics is :
- a)2
- b)3
- c)5
- d)6
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In a survey of 25 students, it was found that 15 had taken Mathematics...
Only Physics = 12-(1+3 +6) = 2
Most Upvoted Answer
In a survey of 25 students, it was found that 15 had taken Mathematics...
Answer:
Given:
A survey of 25 students
Number of students who had taken Mathematics = 15
Number of students who had taken Physics = 12
Number of students who had taken Chemistry = 11
Number of students who had taken Mathematics and Chemistry = 5
Number of students who had taken Mathematics and Physics = 9
Number of students who had taken Physics and Chemistry = 4
Number of students who had taken all the three subjects = 3
To find:
The number of students who had taken only physics
Solution:
Let's represent the given data in a Venn diagram:
From the above Venn diagram, we can observe that:
Number of students who had taken only Mathematics = 15 - 9 - 5 - 3 = -2 (which is not possible)
Number of students who had taken only Physics = 12 - 9 - 4 - 3 = -4 (which is not possible)
Number of students who had taken only Chemistry = 11 - 5 - 4 - 3 = -1 (which is not possible)
Hence, there must be some students who had taken two subjects only i.e., either Mathematics and Physics, Mathematics and Chemistry or Physics and Chemistry.
Let the number of students who had taken Mathematics and Physics only be x.
Then, the number of students who had taken Mathematics and Chemistry only = 5 - x.
And, the number of students who had taken Physics and Chemistry only = 4 - x.
Now, the total number of students can be represented as:
15 = x + 9 + 5 - x + 4 - x + 3 + y
where y is the number of students who had not taken any of these three subjects.
Simplifying the above equation, we get:
y = 1
Therefore, the number of students who had taken only Physics = 12 - 9 - 4 + 3 = 2.
Hence, option (A) is the correct answer.
Given:
A survey of 25 students
Number of students who had taken Mathematics = 15
Number of students who had taken Physics = 12
Number of students who had taken Chemistry = 11
Number of students who had taken Mathematics and Chemistry = 5
Number of students who had taken Mathematics and Physics = 9
Number of students who had taken Physics and Chemistry = 4
Number of students who had taken all the three subjects = 3
To find:
The number of students who had taken only physics
Solution:
Let's represent the given data in a Venn diagram:
From the above Venn diagram, we can observe that:
Number of students who had taken only Mathematics = 15 - 9 - 5 - 3 = -2 (which is not possible)
Number of students who had taken only Physics = 12 - 9 - 4 - 3 = -4 (which is not possible)
Number of students who had taken only Chemistry = 11 - 5 - 4 - 3 = -1 (which is not possible)
Hence, there must be some students who had taken two subjects only i.e., either Mathematics and Physics, Mathematics and Chemistry or Physics and Chemistry.
Let the number of students who had taken Mathematics and Physics only be x.
Then, the number of students who had taken Mathematics and Chemistry only = 5 - x.
And, the number of students who had taken Physics and Chemistry only = 4 - x.
Now, the total number of students can be represented as:
15 = x + 9 + 5 - x + 4 - x + 3 + y
where y is the number of students who had not taken any of these three subjects.
Simplifying the above equation, we get:
y = 1
Therefore, the number of students who had taken only Physics = 12 - 9 - 4 + 3 = 2.
Hence, option (A) is the correct answer.
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In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.The number of students who had taken only physics is :a)2b)3c)5d)6Correct answer is option 'A'. Can you explain this answer?
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In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.The number of students who had taken only physics is :a)2b)3c)5d)6Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.The number of students who had taken only physics is :a)2b)3c)5d)6Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.The number of students who had taken only physics is :a)2b)3c)5d)6Correct answer is option 'A'. Can you explain this answer?.
In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.The number of students who had taken only physics is :a)2b)3c)5d)6Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.The number of students who had taken only physics is :a)2b)3c)5d)6Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.The number of students who had taken only physics is :a)2b)3c)5d)6Correct answer is option 'A'. Can you explain this answer?.
Solutions for In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.The number of students who had taken only physics is :a)2b)3c)5d)6Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
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