| Directions: In each of the following questions two equations are given. You have to solve them and give answer. [SBI Associate (PO) 2007] |
| I. \[12{{p}^{2}}-7p=-1\] |
| II. \[6{{p}^{2}}-7q+2=0\] |
A) If \[p<q\]
B) If \[p>q\]
C) If\[p\le q\]
D) If \[p\ge q\]
E) If \[p=q\]
Correct Answer: A
Solution :
| I. \[12{{p}^{2}}-7p+1=0\] |
| \[\Rightarrow \]\[12{{p}^{2}}-4p-3p+1=0\] |
| \[\Rightarrow \]\[4p\,(3p-1)-1\,(3p-1)=0\] |
| \[\Rightarrow \] \[(4p-1)(3p-1)\]\[\Rightarrow \]\[p=\frac{1}{4},\]\[\frac{1}{3}\] |
| II. \[6{{q}^{2}}-7q+2=0\] |
| \[\Rightarrow \]\[6{{q}^{2}}-4q-3q+2=0\] |
| \[\Rightarrow \]\[2q\,\,(3q-2)-1\,\,(3q-2)=0\] |
| \[\Rightarrow \]\[(2q-1)(3q-2)=0\] |
| \[\Rightarrow \] \[q=\frac{1}{2},\]\[\frac{2}{3}\] |
| \[\therefore \]\[p<q\] |
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