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Question

If x satisfies |x1|+|x2|+|x3|6, then


A

0x4

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B

x2 or x4

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C

x0 or x4

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D

none of these

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Solution

The correct option is C

x0 or x4


We have to solve
|x1|+|x2|+|x3|6
Let |x1|+|x2|+|x3|<6
Now |(x1)+(x2)+(x3)|<|x1|+|x2|+|x3|<6
|3x6|<6|x2|<22<x2<2
or 0<x<4
Hence, for |x1|+|x2|+|x3|6,x0 or x4

Alternative Method:
We have f(x) =|x-1|+|x-2|+|x-3|
To draw the graph of the function, we consider
f(0) =1 +2 +3 =6
f(1) =0 +1 +2 =3
f(2) =1+0+1 =2
f(3) =2 +1 +0 =3
f(4) =3 +2 +1 =6
Now, join these points with line segments as shown in the following figure.
Note: The methods to drew the graphs of such functions is explained in the book "Graphs for JEE Main and JEE Advanced".
Also, draw the line y =6

For f(x)=|x1|+|x2|+|x3|6, graph y=f(x) must lie above the graph of y=6.
As shown in the figure it occurs for x0 or x4


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