I- - x-14 1-91-x is 0- - Which of the above statements is-are true-

The correct option is C both I and II √( x+14 ) lt;x+2 x+14 gt;0 and x+2 gt;0 As √( y ) y gt;0 (1) So we can directly ...

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Byju's Answer

Standard XII

Mathematics

Integration by Substitution

I: √ x+14 <...

Question

I: $\sqrt{x + 14} < x + 2$ is true for $x \in (2, \infty)$ .
II: The solution of the inequation $3^{x + 2} > {(\frac{1}{9})}^{1 / x}$ is $(0, \infty)$ .
Which of the above statement(s) is/are true?

only I

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only II

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both I and II

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neither I nor II

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Solution

The correct option is C both I and II
$\sqrt{x + 14} < x + 2 x + 14 > 0 a n d x + 2 > 0 A s \sqrt{y} y > 0 (1) S o w e c a n d i r e c t l y s q u a r e t h e e q u a t i o n (x + 2)^{2} > (x + 14) x^{2} + 4 x + 4 - x - 14 > 0 x^{2} + 3 x - 10 > 0 (x + 5) (x - 2) > 0 x \in (- \infty, - 5) \cup (2, \infty) A s x > - 2 S o t h e s o l u t i o n s e t i s x \in (2, \infty) P a r t I I 3^{x + 2} > (\frac{1}{9})^{\frac{1}{x}} 3^{x + 2} > (3)^{\frac{- 2}{x}} 3^{x + 2 + \frac{2}{x}} > 3^{0} x + 2 + \frac{2}{x} > 0 \frac{x^{2} + 2 x + 2}{x} > 0 S o t h e s o l u t i o n s e t i s x > 0$

Suggest Corrections

Similar questions

Q. Look at the statements given below:

I.

(3 x + 4 y = 5 and 2 x + 3 y = 9) \Rightarrow (x = - 21 and y = 17)

II.

(x - y + 1 = 0 and 3 x - 5 y + 1 = 0) \Rightarrow (x = - 2 and y = - 1)

III.

(\frac{x}{a} + \frac{y}{b} = 2 and \frac{x}{a} - \frac{y}{b} = 4) \Rightarrow (x = 2 a and y = 2 b)

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(b) II only
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(I)

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(I I I)

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Q. Statement I: Two atoms of X combine with three atoms of Y to form

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Statement II: From the chemical formula of the compound

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Which of the following statement(s) is/are correct?

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(b)

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.Which of the above statement(s) is/are true?

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I: √x+14<x+2 is true for x∈(2,∞).II: The solution of the inequation 3x+2>(19)1/x is (0,∞). Which of the above statement(s) is/are true?

I: $\sqrt{x + 14} < x + 2$ is true for $x \in (2, \infty)$ .
II: The solution of the inequation $3^{x + 2} > {(\frac{1}{9})}^{1 / x}$ is $(0, \infty)$ .
Which of the above statement(s) is/are true?