=e^(z)+1:y^(mu)-y'=0

For a positive number z, if e^(3x)+y^(3)=e^(x)In z^(3y)--In^(3)z and e^(-x)(y+In z)!=-1 then choose the best answer.

If x ,\ y ,\ z are non-zero real numbers, then the inverse of the matrix A=[x0 0 0y0 0 0z] , is [x^(-1)0 0 0y^(-1)0 0 0z^(-1)] (b) x y z[x^(-1)0 0 0y^(-1)0 0 0z^(-1)] (c) 1/(x y z)[x0 0 0y0 0 0z] (d) 1/(x y z)[1 0 0 0 1 0 0 0 1]

if x ne 0 , y ne 0 ,z ne 0 " and " |{:(1+x,,1,,1),(1+y,,1+2y,,1),(1+z,,1+z,,1+3z):}|=0 then x^(-1) +y^(-1) +z^(-1) is equal to

if x ne 0 , y ne 0 ,z ne 0 " and " |{:(1+x,,1,,1),(1+y,,1+2y,,1),(1+z,,1+z,,1+3z):}|=0 then x^(-1) +y^(-1) +z^(-1) is equal to

If x, y, z are all distinct and |(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)),(z,z^(2),1+z^(3))|=0 then value of x y z is :

If tan^(-1)x+tan^(-1)y+tan^(-1)z=pi/2,t h e n x+y+z-x y z=0 x+y+z+x y z=0 x y+y z+z x+1=0 x y+y z+z x-1=0

If tan^(-1)x+tan^(-1)y+tan^(-1)z=pi/2,t h e n x+y+z-x y z=0 x+y+z+x y z=0 x y+y z+z x+1=0 x y+y z+z x-1=0

If tan^(-1)x+tan^(-1)y+tan^(-1)z=pi/2,t h e n (a) x+y+z-x y z=0 (b) x+y+z+x y z=0 (c) x y+y z+z x+1=0 (d) x y+y z+z x-1=0

If x gt 0 , y gt 0 , z gt 0 , the least value of x^(log_(e)y-log_(e)z)+y^(log_(e)z-log_(e)x)+Z^(log_(e)x-log_(e)y) is

If x gt 0 , y gt 0 , z gt 0 , the least value of x^(log_(e)y-log_(e)z)+y^(log_(e)z-log_(e)x)+Z^(log_(e)x-log_(e)y) is