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Let f be a non-negative function defined...

Let f be a non-negative function defined on the interval .[0,1].If `int_0^x sqrt[1-(f'(t))^2].dt`=`int_0^x f(t).dt`, `0<=x<=1` and f(0)=0,then

A

`f ((1)/(2)) lt 1/2 and f ((1)/(3)) gt 1/3`

B

`f ((1)/(2)) gt 1/2 and f ((1)/(3)) gt 1/3`

C

` f ((1)/(2)) lt 1/2 and f ((1)/(3)) lt 1/3`

D

`f ((1)/(2)) gt 1/2 and f ((1)/(3)) lt 1/3 `

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The correct Answer is:
C
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