A) \[{{2}^{10}}\]
B) \[{{10.2}^{9}}\]
C) \[{{10.2}^{10}}\]
D) None of these
Correct Answer: B
Solution :
[b] \[{{(}^{10}}{{C}_{0}})+{{(}^{10}}{{C}_{0}}+{{\,}^{10}}{{C}_{1}})+{{(}^{10}}{{C}_{0}}+{{\,}^{10}}{{C}_{1}}+{{\,}^{10}}{{C}_{2}})\] \[+....+{{(}^{10}}{{C}_{0}}+{{\,}^{10}}{{C}_{1}}+{{\,}^{10}}{{C}_{2}}+...+{{\,}^{10}}{{C}_{9}})\] \[=10{{\,}^{10}}{{C}_{0}}+9{{\,}^{10}}{{C}_{1}}+8{{\,}^{10}}{{C}_{2}}+...+{{\,}^{10}}{{C}_{9}}\] \[={{\,}^{10}}{{C}_{1}}+2{{\,}^{10}}{{C}_{2}}+3{{\,}^{10}}{{C}_{3}}+...10{{\,}^{10}}{{C}_{10}}\] \[=\sum\limits_{r=1}^{10}{{{r}^{10}}{{C}_{r}}=10\sum\limits_{r=1}^{10}{^{9}{{C}_{r-1}}={{10.2}^{9}}}}\]You need to login to perform this action.
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