A) 1
B) 3
C) 7
D) 9
Correct Answer: A
Solution :
[a] Unit's digit in \[({{7}^{4}})=\,1\,.\]Therefore, unit's digit in \[{{({{7}^{4}})}^{8}}\] i.e. \[{{7}^{32}}\] will be 1. Hence, unit's digit in\[{{(7)}^{35}}=1\times 7\times 7\times 7=3\] Again, unit's digit in \[{{(3)}^{4}}=1\] Therefore, unit's digit in the expansion of \[{{({{3}^{4}})}^{17}}={{(3)}^{68}}=\,1\] \[\Rightarrow \]Unit's digit in the expansion of \[({{3}^{71}})=1\times 3\times 3\times 3=7\] And unit's digit in the expansion of \[({{11}^{35}})=1\]Hence, unit's digit in the expansion of\[{{7}^{35}}\times {{3}^{71}}\times {{11}^{55}}=3\times 7\times 1=1\]
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