| Directions: In each of the following questions there are two equations I and II. You have to solve both equations and give answer. [SBI (PO) 2015] |
| I. \[2{{x}^{2}}-15x+28=0\] |
| II. \[2{{y}^{2}}-21y+54=0\] |
A) If \[x>y\]
B) If \[x\ge y\]
C) If \[x<y\]
D) If \[x\le y\]
E) If \[x=y\]or relation cannot be established
Correct Answer: C
Solution :
| I. \[2{{x}^{2}}-15x+28=0\] |
| \[\Rightarrow \] \[2{{x}^{2}}-8x-7x+28=0\] |
| \[\Rightarrow \] \[2x\,(x-4)-7\,(x-4)=0\]\[\Rightarrow \,\]\[x=4,\]\[\frac{7}{2}\] |
| II. \[2{{y}^{2}}-21y+54=0\] |
| \[\Rightarrow \] \[2{{y}^{2}}-12y-9y+54=0\] |
| \[\Rightarrow \] \[2y\,(y-6)-9\,(y-6)=0\]\[\Rightarrow \,\]\[y=6,\]\[\frac{9}{2}\] |
| \[\therefore \] \[x<y\] |
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