The number of integers x,y,z, w such that `x +y+z+w=20 and x , y, w,z ge -1` is

Find x + y + z + w

The number of terms in (2x + 3y + z - w)^20 is

Let N be the number of integral solution of the equation x+y+z+w=15" where " x ge 0, y gt 5, z ge 2 and w ge 1 . Find the unit digit of N.

Let N be the number of integral solution of the equation x+y+z+w=15" where " x ge 0, y gt 5, z ge 2 and w ge 1 . Find the unit digit of N.

The values of x, y, z and w such that [{:(x - y ,2z + w),(2x - y , 2x + w):}] = [{:(6,4),(12,15):}] are

Find x,y,z and w such that [[x-y,2z+w2x-y,2x+w]]=[[5,312,15]]

If 1 , omega , omega^(2) are the cube roots of unity, then prove that ( x + y + z) ( x + y omega + z omega^(2)) ( x + yomega^(2) + z omega) = x^(3) + y^(3) + z^(3) - 3xyz