Question

The value of ${}^{14}{C}_1+{}^{14}{C}_3+{}^{14}{C}_5+.....+{}^{14}{C}_{11}$ is

• A. $2^{14}-1$
• B. $2^{14}-14$
• C. $2^{12}$
• D. $2^{13}-14$

Answer 1

Answer: (D)

${}^{14}{C}_1+{}^{14}{C}_3+{}^{14}{C}_5+....+{}^{14}{C}_{11}$
$=\left({}^{14}{C}_1+{}^{14}{C}_3+{}^{14}{C}_5+....+{}^{14}{C}_{13}\right)-{}^{14}{C}_{13}$
$=2^{14-1}-{}^{14}{C}_1=2^{13}-14$.