[" If "|a_(k)|<3,1<=k<=n," then all complex numbers "z" satisfying equation "1+a_(1)z+a_(2)z^(2)+...+a_(n)z^(n)=0],[[" (A) lie outside circle "|z|=1/4," (B) lie inside circle "|z|=1/4],[" (C) lie on circle "|z|=1/4," (D) lie in "1/3<|z|<|z|<1/2]]

Let f(x)=(a_(2k)x^(2k)+a_(2k-1)x^(2k-1)+...+a_(1)x+a_(0))/(b_(2k)x^(2k)+b_(2k-1)x^(2k-1)+...+b_(1)x+b_(0)) , where k is a positive integer, a_(i), b_(i) in R " and " a_(2k) ne 0, b_(2k) ne 0 such that b_(2k)x^(2k)+b_(2k-1)x^(2k-1)+...+b_(1)x+b_(0)=0 has no real roots, then

Let f(x)=(a_(2k)x^(2k)+a_(2k-1)x^(2k-1)+...+a_(1)x+a_(0))/(b_(2k)x^(2k)+b_(2k-1)x^(2k-1)+...+b_(1)x+b_(0)) , where k is a positive integer, a_(i), b_(i) in R " and " a_(2k) ne 0, b_(2k) ne 0 such that b_(2k)x^(2k)+b_(2k-1)x^(2k-1)+...+b_(1)x+b_(0)=0 has no real roots, then

Given (1-x^(3))^(n)=sum_(k=0)^(n)a_(k)x^(k)(1-x)^(3n-2k) then the value of 3*a_(k-1)+a_(k) is

If a_(k) = (1)/( k(k+1) ) for k= 1,2,3,….n then (sum_(k=1)^(n) a_(k) )=

If a_(k)=(1)/(k(k+1)) for k=1,2,3, .. , n, then (sum_(k=1)^(n) a_(k))^(2)=

Let (1+x^(2))^(2)(1+x)^(n) = sum_(k=0)^(n+4) a_(k) x^(k) . If a_(1) , a_(2) , a_(3) are in A.P., then n=

Let (1+x^(2))^(2)*(1+x)^(n)=sum_(k=0)^(n+4)a_(k)*x^(k) If a_(1),a_(2) and a_(3) are iun AP, find n.