The number of positive integral solutions of the equation `|[x^3+1, x^2y, x^2z] , [xy^2,y^3+1,y^2z] , [xz^2,yz^2,z^3+1]|=30` is

The number of positive integral solutions of the equation det[[x^(3)+1,x^(2)y,x^(2)zxy^(2),y^(3)+1,y^(2)zxz^(2),yz^(2),z^(3)+1]]=30

The number of positive integral solutions of the equation det[[x^(3)+1,x^(2)y,x^(2)zxy^(2),y^(3)+1,y^(2)zxz^(2),z^(2)y,z^(3)+1]]=11

" 4.The number of positive integral solutions of the equation "|[y^(3)+1,y^(2)z,y^(2)x],[yz^(2),z^(3)+1,z^(2)x],[yx^(2),x^(2)z,x^(3)+1]|=11" is "

The number of solutions of the equation.3x+3y-z=5,x+y+z=3,2x+2y-z=3

The number of integral solutions of equation x+y+z+t=29, when x>=1,y>=2,z>=2,3 and t>=0 is

The solutions of the equations x+2y+3z=14,3x+y+2z=11,2x+3y+z=11

The solution of the system of equations is x-y+2z=1,2y-3z=1 and 3x-2y+4y=2 is

The number of solutions of the system of equations: 2x+y-z=7x-3y+2z=1, is x+4y-3z=53(b)2 (c) 1 (d) 0

Prove that |[x,y,z] , [x^2, y^2, z^2] , [yz, zx, xy]| = |[1,1,1] , [x^2, y^2, z^2] , [x^3, y^3, z^3]|