JEE Main & Advanced Mathematics Sets Question Bank Self Evaluation Test - Sets

  • question_answer
    In a group of 500 students, there are 475 students who can speak Hindi and 200 can speak Bengali. What is the number of students who can speak Hindi only?

    A) 275                              

    B) 300

    C) 325                              

    D) 350

    Correct Answer: B

    Solution :

    [b]The number of student = 500 Let H be the set showing number of students who can speak Hindi = 475 and B be the set showing number of students who can speak Bengali = 200 So, \[n(H)=475\] and \[n(B)=200\] and given that \[n(B\cup H)=500\] We have \[n(B\cup H)=n(B)+n(H)-n(B\cap H)\] \[\Rightarrow 500=200+475-n(B\cap H)\] So, \[n(B\cap H)=175\] Hence, persons who speak Hindi only \[=n(H)-n(B\cap H)\] \[=475-175=300\]


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