A) 1
B) 3
C) 5
D) 6
Correct Answer: C
Solution :
[c] \[\left| 2-\left| 1-\left| x \right| \right| \right|=1\Rightarrow 2-\left| 1-\left| x \right| \right|=\pm 1\] \[\Rightarrow \left| 1-\left| x \right| \right|=1\,\,or\,\,3\] If \[\left| \left| 1- \right|x \right|=1\Rightarrow 1-\left| x \right|=\pm 1\Rightarrow \left| x \right|=0\,\,or\,\,2\] \[\Rightarrow x=0\,\,or\,\,\pm 2\] If \[\left| 1-\left| x \right| \right|=3\Rightarrow 1-\left| x \right|=\pm 3\Rightarrow \left| x \right|=-2or4\] \[\Rightarrow \left| x \right|=4\Rightarrow x=\pm 4\] \[[\because \left| x \right|\ne -2]\] \[\therefore \] Solution set is\[\{-4,-2,0,2,4\}\], hence 5 real roots in all.
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