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KVPY Sample Paper KVPY Stream-SX Model Paper-6

  • question_answer
    If \[{{\cos }^{6}}\alpha +{{\sin }^{6}}\alpha +k{{\sin }^{2}}2\alpha =1\,\,(0<\alpha <\pi /2),\] then k is

    A) 3/4

    B)                                ¼

    C) 1/3                               

    D) 1/8

    Correct Answer: A

    Solution :

    The given condition can be written
    \[{{({{\cos }^{2}}\alpha +{{\sin }^{2}}\alpha )}^{3}}-3{{\sin }^{2}}\alpha {{\cos }^{2}}\alpha \,({{\cos }^{2}}\alpha +si{{n}^{2}}\alpha )+\]\[ksi{{n}^{2}}2\alpha =1.\]
    \[\Rightarrow \]   \[(-\,3/4)si{{n}^{2}}2\alpha +ksi{{n}^{2}}2\alpha =0,\]
    showing that \[k=3/4.\]


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