A group of $40$ students appeared in an examination of $3$ subjects - Mathematics, Physics Chemistry. It was found that all students passed in at least one of the subjects, $20$ students passed in Mathematics, $25$ students passed in Physics, $16$ students passed in Chemistry, at most $11$ students passed in both Mathematics and Physics, at most $15$ students passed in both Physics and Chemistry, at most $15$ students passed in both Mathematics and Chemistry. The maximum number of students passed in all the three subjects is___________.
A group of $40$ students appeared in an examination of $3$ subjects - Mathematics, Physics Chemistry. It was found that all students passed in at least one of the subjects, $20$ students passed in Mathematics, $25$ students passed in Physics, $16$ students passed in Chemistry, at most $11$ students passed in both Mathematics and Physics, at most $15$ students passed in both Physics and Chemistry, at most $15$ students passed in both Mathematics and Chemistry. The maximum number of students passed in all the three subjects is___________.
- [JEE MAIN 2024]
- A
$10$
- B
$7$
- C
$5$
- D
$11$
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- [JEE MAIN 2024]
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- [KVPY 2017]