A) \[{{2}^{20}}-{{2}^{10}}\]
B) \[{{2}^{21}}-{{2}^{11}}\]
C) \[{{2}^{21}}-{{2}^{10}}\]
D) \[{{2}^{20}}-{{2}^{9}}\]
Correct Answer: A
Solution :
\[({{\,}^{21}}{{C}_{1}}{{+}^{21}}{{C}_{2}}.....+{{\,}^{21}}{{C}_{10}})\] \[-({{\,}^{10}}{{C}_{1}}{{+}^{10}}{{C}_{2}}.....{{\,}^{10}}{{C}_{10}})\] \[=\frac{1}{2}[({{\,}^{21}}{{C}_{1}}+....+{{\,}^{21}}{{C}_{10}})+({{\,}^{21}}{{C}_{11}}+....{{\,}^{21}}{{C}_{20}})]\] \[-({{2}^{10}}-1)\] \[=\frac{1}{2}[{{2}^{21}}-2]-({{2}^{10}}-1)\] \[=({{2}^{20}}-1)-({{2}^{10}}-1)={{2}^{20}}-{{2}^{10}}\]You need to login to perform this action.
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