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Question

Let f(x)=x26x+5 and m is the number of points of non-derivability of y=|f(|x|)|. If |f(|x|)|=k,kR has at least m distinct solution(s), then the number of integral values of k is

A
2
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B
3
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C
4
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D
5
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Solution

The correct option is C 4
Given : f(x)=x26x+5=(x1)(x5)
Vertex of the parabola
=(b2a,D4a)=(3,4)
The graph of y=|f(|x|)|=|(|x|1)(|x|5)| is


Clearly, y=|f(|x|)| is non-derivable at 5 points.
For |f(|x|)|=k to have at least 5 solutions,
0<k4

Hence, the number of integral values of k is 4.

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