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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)`

Text Solution

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The correct Answer is:
C
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