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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^xsqrt(1-(f^(prime)(t))^2)dt=int_0^xf(t)dt ,0lt=xlt=1,a n d \ 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)`

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

Verified by Experts

The correct Answer is:
C
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