Practice Questions on Inequality...

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1. if, |x - 1| + |x + 1| = 2 , x belongs to

 \begin{array}{l} a)\{ 1\} \\ b)\{ - 1\} \\ c)( - \infty ,1]\\ d)[ - 1,1] \end{array}

2. \frac{{|x + 2| - x}}{x} < 2
\begin{array}{l} a)( - \infty ,0]\bigcup {[2,\infty )} \\ b)[0,2]\\ c)( - \infty ,0]\bigcup {[4,\infty )} \\ d)[2,4] \end{array}

3. \left| {|x - 2| - 1} \right| \ge 3
\begin{array}{l} a)[2,6)\\ b)( - \infty ,2]\bigcup {(4,\infty )} \\ c)( - \infty ,2]\bigcup {[4,\infty )} \\ d)( - \infty ,2]\bigcup {[6,\infty )} \end{array}

4.Solution of {x^2} + x + |x| + 1 \le 0 is :
\begin{array}{l} a)(1,2)\\ b)(0,1)\\ c)\emptyset \\ d)(1,2] \end{array}

5. |x{|^{{x^2} - x - 2}} < 1

\begin{array}{l} a)(1,2)\\ b)(1,\infty )\\ c)( - \infty ,1) \end{array}
d) None of These


6. {2^x} + {2^{|x|}} \ge 2\sqrt 2

\begin{array}{l} a)\left( { - \infty ,{{\log }_2}(\sqrt 2 + 1)} \right)\\ b)(0,\infty ) \end{array}
c)\left( {\frac{1}{2},\log {}_2(\sqrt 2 - 1)} \right)
d)\left( { - \infty ,\log {}_2(\sqrt 2 - 1)} \right)\bigcup {[\frac{1}{2}} ,\infty )





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