A) \[\frac{1}{\sqrt{3}}\]
B) \[\frac{1}{\sqrt{27}}\]
C) \[\sqrt{3}\]
D) 3
Correct Answer: C
Solution :
[c] \[{{3}^{2x-\,y}}={{3}^{x+y}}=\sqrt{27}={{3}^{\frac{3}{2}}}\] \[\Rightarrow \,\,\,2x-\,y=\frac{3}{2}\,\,x+y=\frac{3}{2}\] \[4x-\,2y=3\] \[2x+2y=3\] Solving equation (i) and (ii) \[x=1\] \[y=\frac{1}{2}\] \[\Rightarrow \,\,\,{{3}^{1-\,\frac{1}{2}}}={{3}^{\frac{1}{2}}}=\sqrt{3}\]
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