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 $\lambda$ for which ${x}^{2}-\lambda x+{\mathrm{sin}}^{-1}\left(\mathrm{sin}4\right)>0$ for all $x\in R$, is

1. A

$\varphi$

2. B

(-2, 2)

3. C

$R$

4. D

none of these

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### Solution:

We have,

But, ${\lambda }^{2}+16-4\pi >0$ for all $\lambda \in R$.

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

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