The value of C 1 14 + C 3 14 + C 5 14 + ? + C 11 14 is

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Solution

Q.
The value of ${}^{14}C_{1} + {}^{14}C_{3} + {}^{14}C_{5} + \dots + {}^{14}C_{11}$ is

1 $2^{14} - 1$

2 $2^{14} - 14$

3 $2^{12}$

4 $2^{13} - 14$

Ans.
(4)

${}^{14}C_{1} + {}^{14}C_{3} + {}^{14}C_{5} + \dots + {}^{14}C_{11}$

$= ({}^{14}C_{1} + {}^{14}C_{3} + {}^{14}C_{5} + \dots + {}^{14}C_{13}) - {}^{14}C_{13}$

$= 2^{14 - 1} - {}^{14}C_{1} = 2^{13} - 14$

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