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JEE Main & Advanced Sample Paper JEE Main Sample Paper-9

  • question_answer
    The equations \[{{L}_{1}}\] and \[{{L}_{2}}\] are y = mx and y = nx respectively. Suppose \[{{L}_{1}}\] makes twice as large of an angle with the horizontal (measured counter clock wise from the +ve x-axis) as does \[{{L}_{2}}\] and \[{{L}_{1}}\] has 4 times the slope of \[{{L}_{2}}\]. If \[{{L}_{1}}\] is not horizontal then the value of the product (mn) equals

    A) \[\sqrt{2}/2\]                    

    B) \[-\sqrt{2}/2\]

    C)  2                                            

    D)  -2

    Correct Answer: C

    Solution :

    \[m=\tan 2\theta ,m\ne 0\Rightarrow \theta \ne 0\] \[\tan 2\theta =4\tan \theta \] \[\Rightarrow \]\[\frac{2\tan \theta }{1-{{\tan }^{2}}\theta }=4\tan \theta \Rightarrow {{\tan }^{2}}\theta =\frac{1}{2}\] \[\Rightarrow \]\[mn=\tan 2\theta .\tan \theta =\frac{2{{\tan }^{2}}\theta }{1-{{\tan }^{2}}\theta }=2\]


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