Let `f(x)=1+x^(111)+x^(222)+x^(333)…………….+x^(999)` then `f(x)` is divisible by

Let f(x) be a polynomial function: f(x)=x^(5)+ . . . . if f(1)=0 and f(2)=0, then f(x) is divisible by

Let P(x) and Q(x) be two polynomials.Suppose that f(x) = P(x^3) + x Q(x^3) is divisible by x^2 + x+1, then (a) P(x) is divisible by (x-1),but Q(x) is not divisible by x -1 (b) Q(x) is divisible by (x-1), but P(x) is not divisible by x-1 (c) Both P(x) and Q(x) are divisible by x-1 (d) f(x) is divisible by x-1

Let f : R to and f (x) = (x (x^(4) + 1) (x+1) +x ^(4)+2)/(x^(2) +x+1), then f (x) is :

Let f : R to and f (x) = (x (x^(4) + 1) (x+1) +x ^(4)+2)/(x^(2) +x+1), then f (x) is :

Let f(x)=x+(1)/(x), Then f(x^(3)) equals

Let f(x) = ax^(3) + 5x^(2) - bx + 1 . If f(x) when divide by 2x + 1 leaves 5 as remainder, and f'(x) is divisible by 3x - 1 , then

Let f(x) = ax^(3) + 5x^(2) - bx + 1 . If f(x) when divied by 2x + 1 leaves 5 as remainder, and f'(x) is divisible by 3x - 1, then

Let f(x)=x-1/x" then "f'(-1)