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Question

A real valued differentiable function defined on [1,) where f(1)=1.
If f(x)=1x2+f2(x) then the maximum value of [f(x)] is
(where [.] is greatest integer function)

A
2
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B
1
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C
3
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D
0
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Solution

The correct option is B 1
Since, f(x)>0
f(x) is increasing function.
f(1)=1, f(x)>1
1x2+f2(x)<1x2+1
f(t)f(1)=t11x2+f2(x) dx
f(t)f(1)<11x2+1 dx
f(t)f(1)<tan1x1
f(t)π4<1
f(x)π4<1f(x)<1+π4
Hence [f(x)]=1

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