| Directions: In these questions two equations numbered I and II are given. You have to solve both the equations and give answer. |
| I. \[(6{{x}^{2}}+17)-(3{{x}^{2}}+20)=0\] |
| II. \[(5{{y}^{2}}-12)-(9{{y}^{2}}-16)=0\] |
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: E
Solution :
| I. \[(6{{x}^{2}}+17)-(3{{x}^{2}}+20)=0\] |
| \[\Rightarrow \]\[(6{{x}^{2}}-3{{x}^{2}})+(17-20)=0\] |
| \[\Rightarrow \]\[3{{x}^{2}}-3=0\]\[\Rightarrow \]\[3{{x}^{2}}=3\] |
| \[\therefore \] \[x=\pm 1\] |
| II. \[(5{{y}^{2}}-12)-(9{{y}^{2}}-16)=0\] |
| \[\Rightarrow \]\[(5{{y}^{2}}-9{{y}^{2}})+(-12+16)=0\] |
| \[\Rightarrow \] \[-\,\,4{{y}^{2}}+4=0\] |
| \[\therefore \] \[y=\pm 1\] |
| Hence, \[x=y\] or relationship cannot be established. |
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