The set of values of λ for which x2−λx+sin−1⁡(sin⁡4)>0 for all x∈R, is

The set of values of λ for which x2λx+sin1(sin4)>0 for all xR, is

  1. A

    ϕ

  2. B

    (-2, 2)

  3. C

    R

  4. D

    none of these

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    Solution:

    We have,

    sin1(sin4)=sin1(sin(π4))=π4.x2λx+sin1(sin4)>0 for all xRx2λx+(π4)>0 for all xRλ24(π4)<0λ2+164π<0

    But, λ2+164π>0 for all λR.

    So, there is no value of λ for which the given in equation holds true.

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