Sum of the last 12 coefficients of in the binomial expansion of (1 + x)23 is:

# Sum of the last 12 coefficients of in the binomial expansion of  is:

1. A

${2}^{22}$

2. B

${2}^{23}$

3. C

${2}^{23}{-}^{23}{C}_{11}$

4. D

${2}^{23}-{2}^{11}$

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### Solution:

Sum of last 12 coefficients is

$S{=}^{23}{C}_{12}{+}^{23}{C}_{13}+\dots {+}^{23}{C}_{23}$

Using  we get

$S{=}^{23}{C}_{11}{+}^{23}{C}_{10}+\dots {+}^{23}{C}_{0}$

Adding (1) and (2), we get

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