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JEE Main & Advanced Mathematics Sequence & Series Question Bank Critical Thinking

  • question_answer
    If \[a,\,b,\,c,\,d\] are positive real numbers such that \[a+b+c+d\] \[=2,\] then \[M=(a+b)(c+d)\] satisfies the relation [IIT Screening 2000]

    A) \[0<M\le 1\]

    B) \[1\le M\le 2\]

    C) \[2\le M\le 3\]

    D) \[3\le M\le 4\]

    Correct Answer: A

    Solution :

    \[\frac{(a+b)+(c+d)}{2}\ge \sqrt{(a+b)(c+d)}\] or \[\frac{2}{2}>\sqrt{M}\] or \[1\ge M\] Also\[M>0.\,\,\text{So},\,\,0<M\le 1\].


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