| Directions: In the given questions two equations numbered I and II are given. You have to solve both the equations and mark the appropriate answer. [NICL (AO) 2014] |
| I. \[9{{x}^{2}}-36x+35=0\] |
| II. \[2{{y}^{2}}-15y+27=0\] |
A) \[x\ge y\]
B) \[x<y\]
C) \[x>y\]
D) \[x\le y\]
E) relationship between x and y cannot be determined
Correct Answer: B
Solution :
| I. \[9{{x}^{2}}-36x+35=0\] |
| \[\Rightarrow \] \[9{{x}^{2}}-21x-15x+35=0\] |
| \[\Rightarrow \]\[3x\,(3x-7)-5\,(3x-7)=0\] |
| \[\Rightarrow \] \[(3x-7)(3x-5)=0\] |
| \[\Rightarrow \] \[x=\frac{7}{3},\]\[\frac{5}{3}\] |
| II. \[2{{y}^{2}}-15y+27=0\] |
| \[\Rightarrow \]\[2{{y}^{2}}-6y-9y+27=0\] |
| \[\Rightarrow \]\[2y\,(y-3)-9\,(y-3)=0\] |
| \[\Rightarrow \] \[(y-3)(2y-9)=0\]\[\Rightarrow \]\[y=3,\]\[\frac{9}{2}\] |
| \[\therefore \] \[x<y\] |
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