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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