| Directions: In these questions two equations numbered I and II are given. You have to solve both the equations and find the correct option. |
| I. \[2{{x}^{2}}-13x+21=0\] |
| II. \[5{{y}^{2}}-22y+21=0\] |
A) \[x<y\]
B) \[x>y\]
C) \[k\ge y\]
D) \[k\le y\]
E) Relationship between x and y cannot be established
Correct Answer: C
Solution :
| I. \[2{{x}^{2}}-13x+21=0\] |
| \[\Rightarrow \]\[2{{x}^{2}}-6x-7x+21=0\] |
| \[\Rightarrow \]\[2x\,\,(x-3)-7\,\,(x-3)=0\] |
| \[\Rightarrow \]\[(x-3)\,\,(2x-7)=0\] \[\Rightarrow \]\[x=3,\]\[x=\frac{7}{2}\] |
| II. \[5{{y}^{2}}-22y+21=0\] |
| \[\Rightarrow \]\[5{{y}^{2}}-15y-7y+21=0\] |
| \[\Rightarrow \]\[5y\,\,(y-3)-7\,\,(y-3)=0\] |
| \[\Rightarrow \]\[(5y-7)(y-3)=0\]\[\Rightarrow \]\[y=3,\]\[y=\frac{7}{5}\] |
| Hence, \[x\ge y\] |
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