A) 3
B) \[\frac{1}{3}\]
C) 2
D) \[\frac{1}{2}\]
Correct Answer: B
Solution :
[b] x, y, and z are in G.P. Hene, \[y=xr,\,\,z=x{{r}^{2}}\] Also, x, 2y, and 3z are in A.P. Hence, \[4y=x+3z\] \[\Rightarrow 4xr=x+3x{{r}^{2}}\] \[\Rightarrow 3{{r}^{2}}-4r+1=0\] \[\Rightarrow (3r-1)(r-1)=0\] \[\Rightarrow r=1/3\](\[r\ne 1\]is not possible as x, y, z are distinct)
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