| Directions: In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer. |
| I. \[({{x}^{7/5}}\div 9)=(169\div {{x}^{3/5}})\] |
| II. \[{{y}^{1/4}}\times {{y}^{1/4}}\times 7=273\div {{y}^{1/2}}\] |
A) If \[x>y\]
B) If \[x\ge y\]
C) If \[x<y\]
D) If \[x\le y\]
E) If \[x=y\] or the relationship cannot be established
Correct Answer: D
Solution :
| I. \[\frac{{{x}^{7/5}}}{9}=\frac{169}{{{x}^{3/5}}}\] |
| \[\Rightarrow \]\[{{x}^{(7+3)/5)}}=169\times 9\]\[\Rightarrow \]\[{{x}^{2}}=169\times 9\] |
| \[\Rightarrow \]\[x=\pm \,\,(13\times 3)=\pm \,\,39\] |
| II.\[{{y}^{1/4}}\times {{y}^{1/4}}\times 7=\frac{273}{{{y}^{1/2}}}\] |
| \[\Rightarrow \] \[{{y}^{1/2}}\times 7=\frac{273}{{{y}^{1/2}}}\]\[\Rightarrow \]\[y=\frac{273}{7}=39\] |
| \[\therefore \]\[x\le y\] |
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