If `S` is a set of `P(x)` is polynomial of degree `le2` such that `P(0)=0,P(1)=1,P'(x)gt0,Aaxepsilon(0,1)`, then

Let S denote the set of all polynomials P(x) of degree lt=2 such that P(1)=1,P(0)=0a n dP^(prime)(x)>0AAx in [0,1] , then S=varphi b. S={(1-a)x^2+a x ;0

Let S denote the set of all polynomials P(x) of degree lt=2 such that P(1)=1,P(0)=0a n dP^(prime)(x)>0AAx in [0,1] , then S=varphi b. S={(1-a)x^2+a x ;0

P(x) is said to be a monic polynomial if its leading coefficient is 1. If P(x) is divided b (x-a) the remainder is given by P(a). If P(a) = 0 then (x-a) is called factor of P(x). If P(x) is a monic polynomial of degree 4 such that P(1) = P(2) = P(3) = P(4) = 2. The value of P(0) is

P(x) is said to be a monic polynomial if its leading coefficient is 1. If P(x) is divided b (x-a) the remainder is given by P(a). If P(a) = 0 then (x-a) is called factor of P(x). If P(x) is a monic polynomial of degree 4 such that P(1) = P(2) = P(3) = P(4) = 2. The value of P(5) is

The second degree polynomial f(x), satisfying f(0)=o, f(1)=1,f'(x)gt0AAx in (0,1)

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 polynomial of degree 4 such than P (-1)=P (1) =5 and P (-2) =P(0)=P (2) =2 find the maximum vaue of P (x).

Let p(x) be a polynomial of degree 4 such that P(1)=P(3)=P(5)=P'(7)=0. If the real number ane1,3,5 is such that P(a)=0 can be expressed as a=(p)/(q) , where p and q are relatively prime, then (p-8q) is……….

Let P(x) be a polynomial of degree 11 such that P(x) = (1)/(x + 1) for x = 0, 1, 2, 3,"…."11 . The value of P(12) is.

If A and B are independent events such that P(A) gt 0, P(B) gt 0 , then