" f "a^(1/3)+b^(1/3)+c^(1/3)=0" ,then "

If a^(1/3)+b^(1/3)+c^(1/3)=0 show that (a+b+c)^(3)=27 abc

If a+b+c=1,a^(2)+b^(2)+c^(2)=9 and a^(3)+b^(3)+c^(3)=1, then (1)/(a)+(1)/(b)+(1)/(c) is (i)0 (ii) -1(iii)1(iv)3

Greatest value of f(x)=(x+1)^(1/3)-(x-1)^(1/3) on [0,1] is 1 (b) 2 (c) 3 (d) 1/3

Greatest value of f(x)=(x+1)^(1/3)-(x-1)^(1/3) on [0,1] is 1 (b) 2 (c) 3 (d) 1/3

Greatest value of f(x)=(x+1)^(1/3)-(x-1)^(1/3) on [0,1] is 1 (b) 2 (c) 3 (d) 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 |{:(a,a^2,1+a^3),(b,b^2,1+b^3),(c,c^2,1+c^3):}|=0 , then show that abc=1

If a,b,c are different and |(a,a^(2),a^(3)-1),(b,b^(2),b^(3)-1),(c,c^(2),c^(3)-1)|=0 then

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