A) \[{{2}^{9}}\]
B) \[{{2}^{10}}\]
C) \[{{2}^{10}}-1\]
D) None of these
Correct Answer: A
Solution :
We know that \[{{2}^{n-1}}={{\,}^{n}}{{C}_{0}}+{{\,}^{n}}{{C}_{2}}+{{\,}^{n}}{{C}_{4}}+....={{\,}^{n}}{{C}_{1}}+{{\,}^{n}}{{C}_{3}}+{{\,}^{n}}{{C}_{5}}+.....\] So, \[^{10}{{C}_{1}}+{{\,}^{10}}{{C}_{3}}+{{\,}^{10}}{{C}_{5}}+.....+{{\,}^{10}}{{C}_{9}}={{2}^{10-1}}={{2}^{9}}\]
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