There are $100$ students in a class. In an examination, $50$ of them failed in Mathematics, $45$ failed in Physics, $40$ failed in Biology and $32$ failed in exactly two of the three subjects. Only one student passed in all the subjects. Then the number of students failing in all the three subjects.
- is 12
- is 4
- is 2
- cannot be determined from the given information
The Correct Option is C
Solution and Explanation
$a + b + c + d + e + f + g + h=100$ ...(i)
$h=1$ ...(ii)
$a + b + d +e=50$ ...(iii)
Venn diagram shows failed students
$b + c + d +f=45$ ...(iv)
$d + e + f +g=40$ ...(v)
$b + e +f=32$ ...(vi)
On solving, the above equations, we get $d=2$
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Concepts Used:
Sets
In mathematics, a set is a well-defined collection of objects. Sets are named and demonstrated using capital letter. In the set theory, the elements that a set comprises can be any sort of thing: people, numbers, letters of the alphabet, shapes, variables, etc.
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Elements of a Set:
The items existing in a set are commonly known to be either elements or members of a set. The elements of a set are bounded in curly brackets separated by commas.
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The cardinal number, cardinality, or order of a set indicates the total number of elements in the set.
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