A) \[\frac{1}{2}({{3}^{9}}+4\times {{3}^{8}})\]
B) \[\frac{1}{2}({{3}^{9}}-3)\]
C) \[\frac{1}{2}(7\times {{3}^{8}}-3)\]
D) \[\frac{1}{2}({{3}^{9}}-3+{{3}^{8}})\]
Correct Answer: C
Solution :
[c] Formed number can be utmost of nine digits. Total number of such numbers is \[3+{{3}^{2}}+{{3}^{3}}+...+{{3}^{8}}+2\times {{3}^{8}}\] \[=\frac{3({{3}^{8}}-1)}{3-1}+2\times {{3}^{8}}=\frac{{{3}^{9}}-3+4\times {{3}^{8}}}{2}=\frac{7\times {{3}^{8}}-3}{2}\]
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