| 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. \[2{{p}^{2}}+40=18p\] |
| II. \[{{q}^{2}}=13q-42\] |
A) If \[p=q\]
B) If \[p>q\]
C) If \[p<q\]
D) If \[p\ge q\]
Correct Answer: C
Solution :
| I. \[2{{p}^{2}}+40=18p\] |
| \[\Rightarrow \] \[{{p}^{2}}+20=9p\] |
| \[\Rightarrow \] \[{{p}^{2}}=9p+20=0\] |
| \[\Rightarrow \]\[{{p}^{2}}-4p-5p+20=0\] |
| \[\Rightarrow \]\[p\,\,(p-4)-5\,\,(p-4)=0\] |
| \[\Rightarrow \]\[(p-4)(p-5)=0\]\[\Rightarrow \]\[p=4,\]\[5\] |
| II. \[{{q}^{2}}=13q-42\] |
| \[\Rightarrow \]\[{{q}^{2}}-13q+42=0\] |
| \[\Rightarrow \]\[(q-6)(q-7)=0\]\[\Rightarrow \]\[q=6,\]7 |
| \[\therefore \]\[p<q\] |
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