passage - solve this -3

Let polynomials P_n(x) n=0,1,2,3 ...... , be defined by P₀(x)=1

P_{n}(x) = \frac{1}{n!}\frac{d^{n}}{dx^{n}}[x^{n}(1-x)^{n}] , n\geq 1

Answer the following Q's

1)
The \int_{0}^{1}{P_{n}(x)}x^{k}dx , 0\leq k<n is equla to

a) (n-1)/(k+1)
b) k/(1+n)
c) 0
d) k/ (n+1)(k+1)

2)Let Q(x) be a polynomial of degree n , for which \int_{0}^{1}{Q(x)x^{m}}dx=0
holds for all integers 0\leq m<n

Let c be a constant such that Q(x) -c P_n(x) is of degree (n-1)

then the integral \int_{0}^{1}{(Q(x)-cP_{n}(x))^{2}}dx

is equal to
A) (1+c²)/(n+1)
B) c²/(n+1)
C)0
D)(P_n-1)²

3)Let Q(x) be a polynomail of degree 10 such that \int_{0}^{1}{Q(x)x^{k}}dx = 0 for all integers 0\leq k<9

If Q(0) = 1 , then integral \int_{0}^{1}{(Q(x))^{2}}dx

is equal to
A) 1/21
B)3/21
C)2/7
D)3/7