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,z^2y,z^3+1)|=11` 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),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 solutions of the equations x+2y+3z=14,3x+y+2z=11,2x+3y+z=11

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

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

Show that |(1,x^2,x^3),(1,y^2,y^3),(1,z^2,z^3)| = (x-y),(y-z)(z-x)(xy+yz+zx)

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