| Directions: In the given question two equations numbered I and II are given. You have to solve both the equations and mark the appropriate answer. |
| I. \[2{{x}^{2}}-25x+77=0\] |
| II. \[2{{y}^{2}}-23y+56=0\] |
A) If \[x\ge y\]
B) If \[x<y\]
C) If \[x>y\]
D) If \[x\le y\]
E) relationship between x and y cannot be determined
Correct Answer: E
Solution :
| I. \[2{{x}^{2}}-25x+77=0\] |
| \[\Rightarrow \]\[2{{x}^{2}}-14x-11x+77=0\] |
| \[\Rightarrow \]\[2x\,(x-7)-11\,(x-7)=0\] |
| \[\Rightarrow \] \[(x-7)(2x-11)=0\Rightarrow x=7,\]\[\frac{11}{2}\] |
| II. \[2{{y}^{2}}-23y+56=0\] |
| \[\Rightarrow \]\[2{{y}^{2}}-16y-7y+56=0\] |
| \[\Rightarrow \]\[2y\,(y-8)-7\,(y-8)=0\] |
| \[\Rightarrow \] \[(y-8)(2y-7)=0\Rightarrow y=8,\]\[\frac{7}{2}\] |
| Hence, relationship between x and y cannot be determined. |
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