The middle term in the expansion of $(1 + x)^{2 n}$ is

^{2 n} C_{n}

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^{2 n} C_{n - 1} . x^{n + 1}

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^{2 n} C_{n - 1} . x^{n - 1}

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^{2 n} C_{n} . x^{n}

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Solution

The correct option is D $^{2 n} C_{n} . x^{n}$
Middle term $= \frac{N}{2} + 1$
$= \frac{2 n}{2} + 1$
$= (n + 1)^{t h}$ term
Now consider the following,
$T_{r + 1} =^{n} C_{r} a^{n - r} b^{r}$ ...(i)
Where $T$ represents the term
Here the middle term is the $(n + 1)^{t h}$ term
Hence $r + 1 = n + 1$
$∴ r = n$
Substituting in (i), we get $^{2 n} C_{n} 1^{2 n - n} x^{n}$
$=^{2 n} C_{n} x^{n}$
Hence answer is D

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