If `(1+x+2x^(2))^(20) =a_(0)+a_(1)x+a_(2)x^(2) +a_(3)x^(3)+….+a_(40)x^(40),`
then find the value of `a_(1)+a_(3)+a_(5)+….+a_(39)`.

If (1+x-2x^(2))^(6)=1+a_(1)x+a_(2)x^(2)+….+a_(12)^(x^(12)) , then find the value of a_(2)+a_(4)+a_(6)+….+a_(12) .

If |(x^(2)+x, 3x-1, -x+3),(2x+1, 2+x^(2),x^(3)-3),(x-3, x^(2)+4, 3x)| = a_(0) + a_(1)x + a_(2)x^(2) +….+a_(7)x^(7) , then the value of a_(0) is a)25 b)24 c)23 d)21

If a_(n+1)= (1)/(1-a_(n)) for n gt=1 and a_(3) = a_(1) then find the value of (a_(2001))^(2001) .

Let (1+x)^(n) = 1+a_(1)x + a_(2)x^(2) + ……+ a_(n)x^(n) . If a_(1), a_(2) and a_(3) are in AP, then the value of n is

Let a_(1), a_(2),a_(3), cdots , a_(4001) are in A.P. such that (1)/(a_(1)a_(2))+(1)/(a_(2)a_(3))+ cdots + (1)/(a_(4000) a_(4001))= 10 and a_(2)+ a_(4000) = 50 then find the value of |a_(1)-a_(4001)| .

If (2x^(2)-x-1)^(5)=a_(0)+a_(1)x+a_(2)x^(2)+…+a_(10)x^(10) , then a_(2)+a_(4)+a_(6)+a_(8)+a_(10) is equal to : a)15 b)30 c)16 d)32

Let P(x) = a_(0) + a_(1)x^(2) + a_(2)x^(4)+...+a_(n)x^(2n) be a polynomial in a real variable x with 0 lt a_(0) lt a_(1) lt a_(2) lt ... lt a_(n) . The function P(x) has