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,2q,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

Find the value of x, y, z if [(x, y-z, z+3)]+[(y, 4, 3)]

Given that x ,y ,z are positive real such that x y z=32. If the minimum value of x^2+4x y+4y^2+2z^2 is equal m , then the value of m//16 is.

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 sin^(-1) X+ sin^(-1) y+ sin^(-1) z= pi , then prove that x^4 +y^4+ z^4 +4x^2 y^2 z^2 = 2(x^2 y^2 +y^2 z^2+z^2x^2).

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

Find GCD of 25x^(2) y^(2)z, 45x^(2) y^(4) z^(3) b