If the points `(alpha-x,alpha,alpha) , (alpha,alpha-y,alpha)` and `(alpha, alpha, alpha-z)` are coplanar then

If alpha is a cube of unity , then the value of |{:(alpha,alpha^(3),alpha^(5)),(alpha^(3),alpha^(5),alpha),(alpha^(5),alpha,alpha^(3)):}| is equal to

If alpha is a cube root of unity , then find the value of |{:(alpha,alpha^3,alpha^5),(alpha^3,alpha^5,alpha),(alpha^5,alpha,alpha^3):}|

If a,b,c are non-zero,then the system of equations (alpha+a)x+alpha y+alpha z=0,alpha x+(alpha+b)y+alpha z=0,alpha x+alpha y+(alpha+c)z=0 has a non-trivial solution if alpha^(-1)=(A)-(a^(-1)+b^(-1)+c^(-1))(B)a+b+c (C) alpha+a+b+c=1 (D) none of these

If a,b,are non-zeroes then the system of equations (alpha+a)x+alpha y+alpha z=0alpha x+(alpha+b)y+alpha z=0alpha x+alpha y+(alpha+c)z=0

Find the coefficient of alpha^(6) in the product (1+alpha+alpha^(2))(1+alpha+alpha^(2))(1+alpha+alpha^(2)+alpha^(3)) (1+alpha)(1+alpha)(1+alpha) .

Find the coefficient of alpha^(6) in the product (1+alpha+alpha^(2))(1+alpha+alpha^(2))(1+alpha+alpha^(2)+alpha^(3)) (1+alpha)(1+alpha)(1+alpha) .

Find the coefficient of alpha^(6) in the product (1+alpha+alpha^(2))(1+alpha+alpha^(2))(1+alpha+alpha^(2)+alpha^(3)) (1+alpha)(1+alpha)(1+alpha) .