The function f(x)=min{sin√[m]x,|x|} and f(x) has period of π where [⋅] denotes greatest integer function , then
A
m∈{4}
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B
m∈[3,4)
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C
m∈[4,5)
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D
None of these
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Solution
The correct option is Dm∈[4,5) Given f(x)=min{sin√[m]x,|x|} ⇒f(x)=sin√[m]x(∵sinpx≤|x|∀p,x) Given ,period of sin√[m]x=π ∴2π√[m]=π ⇒[m]=4 ⇒mϵ[4,5)i.e.4≤m<5