A) 1
B) \[-1\]
C) 0
D) \[\frac{1}{2}\]
Correct Answer: B
Solution :
Given that, \[x+\frac{1}{y}=1\] \[\Rightarrow \] \[xy+1=y\] ?...(i) and \[y+\frac{1}{z}=1\] \[\Rightarrow \] \[1-\frac{1}{z}=y\] \[\Rightarrow \] \[\frac{z-1}{z}=y\] ?...(ii) From eq. (ii), \[y=\frac{z-1}{z}\] Comparing eqn. (i) with (ii) \[xy+1=\frac{z-1}{z}\] \[\Rightarrow \] \[xyz+z=z-1\] \[\Rightarrow \] \[xyz=-1\]
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