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J & K CET Engineering J and K - CET Engineering Solved Paper-2005

  • question_answer
    In a class of 30 pupils. 12 take needls 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

    A)  \[16\]          

    B)  \[6\]

    C)  \[8\]             

    D)  \[20\]

    Correct Answer: A

    Solution :

    Given that \[n(N)=12,\,n(P)=16,\,n(H)=18,\] \[n(N\cup P\cup H)=30\] and \[n(N\cap P\cap H)=0\] Now, \[n(N\cup P\cup H)=n(N)+n(P)+n(H)\] \[-n(N\cup P)-n(P\cap H)-n(H\cap N)\] \[+n(N\cap P\cap H)\] \[\Rightarrow \] \[n(N\cap P)+N(P\cap H)+N(H\cap N)\] \[=n(N)+n(P)+n(H)-n(N\cup P\cup H)\] \[=(12+16+18)-30\] \[=46-30=16\]


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