| Assertion (A): If HCF \[(209,737)=11\] and LCM \[(209,737)=209\times R,\] then the value of R is 68. |
| Reason (R): For any two positive numbers a and b, HCF \[(a,b)\times LCM\,(a,b)=a\times b.\] |
A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A)
C) Assertion (A) is true but reason (R) is false
D) Assertion (A) is false but reason (R) is true
Correct Answer: D
Solution :
| Sol. [d] Given, \[HCF(209,\,737)=11\] and \[LCM(209,\,737)=209\times R\] |
| \[\therefore \,\,\,\,\,\,\,\,\,\,LCM(209,737)=\frac{209\times 737}{HCF(209,737)}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,209\times R=\frac{209\times 737}{11}\Rightarrow R=\frac{737}{11}=67\] |
| \[\therefore \] Assertion: False; Reason: True. |
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