A) 0
B) 1
C) 49
D) 341
Correct Answer: B
Solution :
\[{{7}^{84}}/342={{({{7}^{3}})}^{28}}/({{7}^{3}}-1)\] \[=({{({{7}^{3}})}^{28}}-1+1)/({{7}^{3}}-1)\] \[=({{({{7}^{3}})}^{28}}-1)/({{7}^{3}}-1)+1/({{7}^{3}}-1)\] \[=({{({{7}^{3}})}^{28}}-1)/({{7}^{3}}-1)\] is always divisible as it is in the form of \[({{x}^{n}}-{{y}^{n}})/(x-y).\] hence the remainder is 1.
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