Each of the following inequalities is true for some values of $x$ EXCEPT

x < x^{2} < x^{3}

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x < x^{3} < x^{2}

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x^{2} < x^{3} < x

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x^{3} < x < x^{2}

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x^{3} < x^{2} < x

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Solution

The correct option is B $x^{2} < x^{3} < x$
$x < x^{2} < x^{3}$ is true for $x > 1$
$x < x^{3} < x^{2}$ is true for $- 1 < x < 0$
$x^{2} < x^{3} < x$ is not true for all values of $x$
$x^{3} < x < x^{2}$ is true for $x < - 1$
$x^{3} < x^{2} < x$ is true for $0 < x < 1$
Therefore option $C$ is correct

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Similar questions

Determine which of the following polynomials have $(x + 2)$ as a factor:

Q. If

\frac{x^{3} + x^{2} + x + 1}{x^{3} - x^{2} + x - 1} = \frac{x^{2} + x + 1}{x^{2} - x + 1}

, then the number of real-value of

x

satisfying are

Q. Show that

\frac{X^{3} + X^{2} + X + 1}{X^{3} - X^{2} + X - 1}

=

\frac{X^{2} + X + 1}{X^{2} - X + 1}

, is not possible for any

X

ϵ

Q. x + 1 is a factor of the polynomial
(a) x³ + x²– x + 1
(b) x³ + x² + x + 1
(c) x⁴ + x³ + x² + 1
(d) x⁴ + 3x³ + 3x² + x + 1

$x + 1$ is a factor of the polynomial
$A .$ $x^{3} + x^{2} - x + 1$
$B .$ $x^{3} + x^{2} + x + 1$
$C .$ $x^{4} + x^{3} + x^{2} + 1$
$D .$ $x^{4} + 3 x^{3} + 3 x^{2} + x + 1$

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Each of the following inequalities is true for some values of x EXCEPT

The correct option is B x2<x3<xx<x2<x3 is true for x>1x<x3<x2 is true for −1<x<0x2<x3<x is not true for all values of xx3<x<x2 is true for x<−1x3<x2<x is true for 0<x<1Therefore option C is correct

Each of the following inequalities is true for some values of $x$ EXCEPT