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KVPY Sample Paper KVPY Stream-SX Model Paper-4

  • question_answer
    If \[x=\frac{4\lambda }{1+{{\lambda }^{2}}}\] and \[y=\frac{2-2{{\lambda }^{2}}}{1+{{\lambda }^{2}}}\] where a is a real parameter and \[{{x}^{2}}-xy+{{y}^{2}}\] lies between [a, b] then (a + b) is-

    A) 8

    B) 10  

    C) 13                                

    D) 25

    Correct Answer: A

    Solution :

    [A]
    Let \[\lambda =\tan \theta \]
    \[\therefore x=2sin2\theta \]
    \[y=2\cos 2\theta \]
    \[\therefore {{x}^{2}}+{{y}^{2}}-xy=4-2\sin \,\,4\theta \]
    \[{{x}^{2}}+{{y}^{2}}-xy\in [2,6]\]
    \[\therefore a+b=8\]


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