The exhaustive set of values of - such that lnx2-2x-2 2-lnx2-2x-2-1 -0 - x-1 is

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Standard XII

Mathematics

Properties of Set Operation

The exhaustiv...

Question

The exhaustive set of values of $λ$ such that ${(ln (x^{2} - 2 x + 2))}^{2} + λ ln (x^{2} - 2 x + 2) + 1 > 0 \forall x > 1$ is

(- 3, \infty)

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(- 1, \infty)

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(- 2, 2)

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[- 1, \infty)

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Solution

The correct option is C $(- 2, 2)$

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lf the angle $θ$ between the line $\frac{x + 1}{1} = \frac{y - 1}{2} = \frac{z - 2}{2}$ and the plane $2 x - y + \sqrt{λ} z + 4 =$ $0$ is such that $sin θ = \frac{1}{3}$ , then value of $λ$ is

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\frac{x + 1}{1} = \frac{y - 1}{2} = \frac{z - 2}{2}

and the plane

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Q. If the angle

θ

between the line

\frac{x + 1}{1} = \frac{y - 1}{2} = \frac{z - 2}{2}

and the plane

2 x - y + \sqrt{λ} z + 4 = 0

is such that

sin θ = \frac{1}{3}

, then value of

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The exhaustive set of values of λ such that (ln(x2−2x+2))2+λln(x2−2x+2)+1>0 ∀x>1 is

The correct option is C (−2,2)

The exhaustive set of values of $λ$ such that ${(ln (x^{2} - 2 x + 2))}^{2} + λ ln (x^{2} - 2 x + 2) + 1 > 0 \forall x > 1$ is

The correct option is C $(- 2, 2)$