P(x) is a non-zero polynomial such that P(0)=0 and `P(x^3)=x^4P(x).P'(1)=7` and `int_0^1P(x)=1.5` then `int_0^1P(x) P'(x) dx =`

If P(x) is a polynomial such that P(x^(2)+1)={P(x)}^(2)+1 and P(0)=0, then P'(0) is equal to

If P(x) is a polynomial such that P(x^(2)+1)={P(x)}^(2)+1 and P(0)=0, then P'(0) is equal to

If p(x) is a polynomial such that p(x^2+1)={p(x)}^2+1 and p(0)=0 then p^1(0) is equal to

Let P(x) be a function defined on R such that P(x) = P'(1--x), AA x in [0, 1], P(0)=1, P(1) =41 then int_(0)^(1)P(x)dx=

If P (x) is polynomial of degree 2 and P(3)=0,P'(0)=1,P''(2)=2," then "p(x)=

Let P be a non-zero polynomial such that P(1+x)=P(1-x) for all real x, and P(1)=0. Let m be the largest integer such that (x-1)^m divides P(x) for all such P(x). Then m equals

Let p(x) be a function defined on R such that p'(x) = p' (1 - x) , for all x in [0,1], p(0) = 1 and p (1) = 41. Then int_0^1 p(x) dx equals :

If P(x) is a cubic polynomial with P(1)=3,P(0)=2 and P(-1)=4, then underset(-1)overset(1)fP(x)dx is

P(x) is a least degree polynomial such that (P(x)-1) in divisible by (x-1)^(2) and (P(x)-3) is divisible by ((x+1)^2) ,then (A) graph of y=P(x) ,is symmetric about origin (B) y=P(x) ,has two points of extrema (C) int_(-1)^(2)P(x)dx=0 for exactly one value of lambda . (D) int_(-1)^(2)P(x)dx=0 for exactly two values of lambda