If `x!=y!=za n d|xx^2 1+x^3y y^2 1+y^3z z^2 1+z^3|=0,` then the value of `x y z` is `1` b. `2` c. `-1` d. `2`

If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, then the value of x y z is a.1 b. 2 c. -1 d. 2

If |{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z, z^2,1+z^3):}|=0 then relation of x,y and z is

If x=3, y=2 and z=-1 , then the value of (x^3+y^3+1)/(y^3-z^3) is

Let =|A xx^2 1B y y^2 1C z z^2 1|a n d_1=|A B C x y z y z z xx y|, then show that _1=

If |(x, x^2, x^3 +1), (y, y^2, y^3+1), (z, z^2, z^3+1)| = 0 and x ,y and z are not equal to any other, prove that, xyz = -1

If x y z=0, then find the value of (a^x)^(y z)+(a^y)^(z x)+(a^z)^(x y)= (a)3 (b) 2 (c)1 (d) 0

x+y+z=1 x-2y+3z=2 5x-3y+z=3