A) 2
B) 1
C) 0
D) 8
E) 9
Correct Answer: B
Solution :
\[{{(19)}^{2005}}+{{(11)}^{2005}}-{{(9)}^{2005}}\] \[={{(10+9)}^{2005}}+{{(10+1)}^{2005}}-{{(9)}^{2005}}\] \[=({{9}^{2005}}{{+}^{2005}}{{C}_{1}}{{(9)}^{2004}}\times 10+....)\] \[+{{(}^{2005}}{{C}_{0}}{{+}^{2005}}{{C}_{1}}10+......)-{{(9)}^{2005}}\] \[={{(}^{2005}}{{C}_{1}}{{9}^{2004}}\times 10.....multiple\,of\,10)\] + 1 + multiple of 10 \[\therefore \] Unit digit =1
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