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 (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-3x^(2))^(10)=1+a_(1)x+a_(2)x^(2)+....+a_(20)x^(20),"then "a_(2)+a_(4)+a_(6)+...+a_(20) is equal to a) (3^(10)+1)/(2) b) (3^(9)+1)/(2) c) (3^(10)-1)/(2) d) (3^(9)-1)/(2)

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 (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

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) .

Three distinct A.P. s' have same first term common differences as d_(1) ,d_(2) ,d_(3) and n^(th) terms as a_(n) , b_(n) ,c_(n) respectively such that (a_(1))/(d_(1))=(2b_(1))/(d_(2))=(3c_(1))/(d_(3)). If (a_(7))/(c_(6))=(3)/(7) then find the value of (b_(7))/(c_(6)) .