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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2005

  • question_answer
        \[{{\sin }^{2}}\theta =\frac{4xy}{{{(x+y)}^{2}}}\]is true if and only if:

    A)  \[x+y\ne 0\]                     

    B)  \[x=y,x\ne 0,y\ne 0\]

    C)  \[x=y\]               

    D)  \[x\ne 0,y\ne 0\]

    Correct Answer: B

    Solution :

                    We know that \[{{\sin }^{2}}\theta \ge 1\] \[\frac{4xy}{{{(x+y)}^{2}}}\ge 1\] \[\Rightarrow \]               \[4xy\ge {{(x+y)}^{2}}\] \[\Rightarrow \]               \[{{(x-y)}^{2}}\le 0\] \[\Rightarrow \]               \[x-y=0\] \[\Rightarrow \]               \[y=x\] and        \[x\equiv 0,y\ne 0\]


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