" 4.The number of positive integral solu...

" 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 "

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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

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

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

|[yz,x,x^(2)],[zx,y,y^(2)],[xy,z,z^(2)]|=|[1,x^(2),x^(3)],[1,y^(2),y^(3)],[1,z^(2),z^(3)]|

" (d) "|[x,y,z],[x^(2),y^(2),z^(3)],[yz,zx,xy]|=|[1,1,1],[x^(3),y^(2),z^(2)],[x^(3),y^(3),z^(3)]|

|[1/x,1/y,1/z],[x^(2),y^(2),z^(2)],[yz,zx,xy]|

Solve the following equations: x+y+z=a ,x^(2)+y^(2)+z^(2)=a^(2),x^(3)+y^(3)+z^(3)=a^(3)

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

If x.y,z are positive real numbers such that x^(2)+y^(2)+z^(2)=27, then x^(3)+y^(3)+z^(3) has