Find the greatest value of `x^2y^3z^4` if `x^2+y^2+z^2=1,w h e r ex ,y ,z` are positive.

The value of |[yz, z x,x y],[ p,2p,3r],[1, 1, 1]|,w h e r ex ,y ,z are respectively, pth, (2q) th, and (3r) th terms of an H.P. is a.-1 b. 0 c. 1 d. none of these

If x,y,z are positive intergers and x+y+z=240 and x^2 + y^2= z^2 then find the number of positive solutions.

Find the coffiecient of x^2 y^3 z^4 w in the expansion of (x-y-z+w)^(10)

Find the number of integral solutions of x+y+z+y 2,y>1,z>=2,w>=0

Find the value of x,y, and z if : (i) [[3,x4,y]]=2.[[-1.5,1z,1]]

Find the value of (( x -y )^3 + ( y - z )^3 + ( z - x )^3 )/ (9 ( x - y )( y - z ) ( z - x )) 1 . 0 2 . 1/9 3 . 1/3 4. 1

If x^2 + y^2 + z^2 =2 (x-y-z) - 3, then the value of 2x - 3y + 4z is [Assume that x, y, z are all real numbers] :