| Directions: In these questions two equations numbered I and II are given. You have to solve both the equations and give answer. |
| I. \[6{{x}^{2}}-29x+35=0\] |
| II. \[3{{y}^{2}}-11y+10=0\] |
A) If \[x\ge y\]
B) If \[x<y\]
C) If \[x\ge y\]
D) If \[x>y\]
E) If \[x=y\]or relationship cannot be established
Correct Answer: D
Solution :
| I. \[6{{x}^{2}}-29x+35=0\] |
| \[\Rightarrow \]\[6{{x}^{2}}-15x-14x+35=0\] |
| \[\Rightarrow \]\[3x\,\,(2x-5)-7\,\,(2x-5)=0\] |
| \[\Rightarrow \]\[(3x-7)(2x-5)=0\] |
| \[\Rightarrow \]\[x=\frac{7}{3},\]\[\frac{5}{2}\] |
| II. \[3{{y}^{2}}-11y+10=0\] |
| \[\Rightarrow \]\[3{{y}^{2}}-6y-5y+10=0\] |
| \[\Rightarrow \]\[3y\,\,(y-2)-5\,\,(y-2)=0\] |
| \[\Rightarrow \]\[(3y-5)(y-2)=0\]\[\Rightarrow \]\[y=\frac{5}{3},\]\[y=2\] |
| Hence, \[x>y\] |
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