If `x ,y ,a n dz` are real and different and `u=x^2+4y^2+9z^2-6y z-3z x-2x y ,t h e nu` is always a. non-negative b. zero c. non-positive d. none of these

If x ,y ,z are real and 4x^2+9y^2+16 z^2-6x y-12 y z-8z x=0,t h e nx , y,z are in a. A.P. b. G.P. c. H.P. d. none of these

If x ,y ,a n dz are positive real umbers and x=(12-y z)/(y+z) . The maximum value of x y z equals.

If x ,y ,a n dz are pth, qth, and rth terms, respectively, of an A.P. nd also of a G.P., then x^(y-z)y^(z-x)z^(x-y) is equal to x y z b. 0 c. 1 d. none of these

The least value of the expression x^2+4y^2+3z^2-2x-12 y-6z+14 is a. 3 b. no least value c. 0 d. none of these

The least value of the expression x^2+4y^2+3z^2-2x-12 y-6z+14 is a. 1 b. no least value c. 0 d. none of these

If x ,y ,z are different from zero and "Delta"=a b-y c-z a-x b c-z a-x b-y c=0, then the value of the expression a/x+b/y+c/z is 0 b. -1 c. 1 d. 2

If x,y,z are positive real numbers such that x^(2)+y^(2)+Z^(2)=7 and xy+yz+xz=4 then the minimum value of xy is

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.

If w(x,y,z) = x^2y+y^2z + z^2x,x,y,z in R, find the differential dw.