Let `f` be a non-negative function defined on the interval `[0,1]`. If `int_0^xsqrt(1-(f\'(t))^2)dt=int_0^xf(t)dt, 0lexle1` and `f(0)=0`, then (A) `f(1/2)lt1/2` and `f(1/3)gt1/3` (B) `f(1/2)gt1/2` and `f(1/3)gt1/3` (C) `f(1/2)lt1/2` and `f(1/3)lt1/3` (D) `f(1/2)gt1/2` and `f(1/3)lt1/3`

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

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 le x le 1 and f(0) = 0, then :

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

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

Let f be a non-negative function defined on the interval [0,1]dot If int_0^xsqrt(1-(f^(prime)(t))^2)dt=int_0^xf(t)dt ,0lt=xlt=1,a n df(0)=0,t h e n (A)f(1/2) 1/3 (B)f(1/2)>1/2a n df(1/3)>1/3 (C)f(1/2) 1/2a n df(1/3)<1/3

Let f be a non-negative function defined on the interval [0,1]dot If int_0^xsqrt(1-(f^(prime)(t))^2)dt=int_0^xf(t)dt ,0lt=xlt=1,a n df(0)=0,t h e n (A) f(1/2) 1/3 (B) f(1/2)>1/2a n df(1/3)>1/3 (C) f(1/2) 1/2a n df(1/3)<1/3

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)

If int_(0)^(1) f(t)dt=x^2+int_(0)^(1) t^2f(t)dt , then f'(1/2)is