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JEE Main & Advanced Mathematics Sets Question Bank Set theory

  • question_answer
    In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is [DCE 1993; ISM Dhanbad 1994]

    A) 22

    B) 33

    C) 10

    D) 45

    Correct Answer: D

    Solution :

    \[n\,(M)=55,n\,(P)=67,n\,(M\cup P)=100\] Now, \[n\,(M\cup P)=n\,(M)+n\,(P)-n\,(M\cap P)\] \[100=55+67-n\,(M\cap P)\] \\[n\,(M\cap P)=122-100=22\] Now n (P only) =\[n\,(P)-n(M\cap P)\]\[=67-22=45\].


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