Given `a=x//(y-z), b=y//(z-x), and c=z//(x-y),w h e r e .x , y and z` are not all zero, then the value of `a b+b c+c a` is a.`0` b. `1` c.`-1""` d. none of these

If x=c y+b z ,y=a z+c x ,z=x+a y ,w h e r e .x ,y ,z are not all zeros, then find the value of a^2+b^2+c^2+2a b c dot

a ,b ,c are distinct real numbers not equal to one. If a x+y+z=0,x+b y+z=0, and x+y+c z=0 have nontrivial solution, then the value of 1/(1-a)+1/(1-b)+(1)/(1-c) is equal to a. 1 b. -1 c. z e ro d. none of these

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

Value of |x+y z z x y+z x y y z+x|,w h e r ex ,y ,z are nonzero real number, is equal to x y z b. 2x y z c. 3x y z d. 4x y z

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 a ,b ,c are in G.P. and a^(1//x)=b^(1//y)=c^(1//z), then x y z are in AP (b) GP (c) HP (d) none of these

If a,b and c are A.P. whereas x,y and z are in G.P. : Prove that : x^(b-c)*y^(c-a)*z^(a-b)=1 .

Comprehension 1 Let x ,\ y ,\ z in R^+&\ D=|xx^3x^4-1y y^3y^4-1z z^3z^4-1| If x!=y!=z\ &\ x ,\ y ,\ z are in A.P. and D=o,\ t h e n\ 2x^2z+x^2z^2 is equal to a. 1 b. 2 c. 3\ d. none of these

If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1

If x , y , z are not all zero such that a x+y+z=0 , x+b y+z=0 , x+y+c z=0 then prove that 1/(1-a)+1/(1-b)+1/(1-c)=1