| Directions: In each question below one or more equation (s) is / are provided. On the basis of these you have to find out relation between p, q and give answer. [SBI (PO) 2000] |
| I. \[4{{q}^{2}}+8q=4q+8\] |
| II. \[{{p}^{2}}+9p=2p-12\] |
A) If \[p=q\]
B) If \[p>q\]
C) If \[p<q\]
D) If \[p\ge q\]
Correct Answer: C
Solution :
| I. \[4{{q}^{2}}+8q=4q+6\] |
| \[\Rightarrow \]\[4{{q}^{2}}+4q-8=0\] |
| \[\Rightarrow \]\[{{q}^{2}}+q-2=0\] |
| \[\Rightarrow \]\[{{q}^{2}}+2q-q-2=0\] |
| \[\Rightarrow \]\[q\,\,(q+2)-1\,\,(q+2)=0\] |
| \[\Rightarrow \]\[(q+2)(q-1)=0\]\[\Rightarrow \]\[q=-\,2,1\] |
| II. \[{{p}^{2}}+9p=2p-12\] |
| \[\Rightarrow \]\[{{p}^{2}}+7p+12=0\] |
| \[\Rightarrow \]\[{{p}^{2}}+3p+4p+12=0\] |
| \[\Rightarrow \]\[p\,\,(p+3)+4\,\,(p+3)=0\] |
| \[\Rightarrow \]\[(p+3)(p+4)=0\]\[\Rightarrow \]\[p=-\,3,\]\[-\,\,4\] |
| \[\therefore \]\[p<q\] |
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