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JEE Main & Advanced Mathematics Sets Question Bank Set theory

  • question_answer
    In a class of 30 pupils, 12 take needle work, 16 take physics and 18 take history. If all the 30 students take at least one subject and no one takes all three then the number of pupils taking 2 subjects is [J & K 2005]

    A) 16

    B) 6

    C) 8

    D) 20

    Correct Answer: A

    Solution :

    Given\[n(N)=12\], \[n(P)=16\], \[n(H)=18\], \[n(N\cup P\cup H)=30\] From, \[n(N\cup P\cup H)=n(N)+n(P)+n(H)-n(N\cap P)\] \[-n(P\cap H)-n(N\cap H)+n(N\cap P\cap H)\] \ \[n(N\cap P)+n(P\cap H)+n(N\cap H)=16\] Now, number of pupils taking two subjects \[=n(N\cap P)+n(P\cap H)+n(N\cap H)-3n(N\cap P\cap H)\] \[=16-0=16\].


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