The coefficient of the middle term in the exp | vedclass

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(B) The binomial expansion of $(1 + x)^n$ has $n+1$ terms.Here,$n = 10$,which is an even number,so the total number of terms is $10 + 1 = 11$.Since th

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$\frac{10!}{(5!)^2}$

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(B) The binomial expansion of $(1 + x)^n$ has $n+1$ terms.Here,$n = 10$,which is an even number,so the total number of terms is $10 + 1 = 11$.Since the number of terms is odd,there is only one middle term,which is the $\left( \frac{n}{2} + 1 \right)^{th}$ term.Middle term $= \left( \frac{10}{2} + 1 \right)^{th} = 6^{th}$ term.The general term $T_{r+1}$ in the expansion of $(1 + x)^n$ is given by $T_{r+1} = {}^nC_r x^r$.For the $6^{th}$ term,$r+1 = 6$,so $r = 5$.$T_6 = {}^{10}C_5 x^5$.The coefficient of the middle term is ${}^{10}C_5 = \frac{10!}{5!(10-5)!} = \frac{10!}{(5!)^2}$.

The coefficient of the middle term in the expansion of $(1 + x)^{10}$ is

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