(C) Given expression is $(1 + 3x + 3x^2 + x^3)^6$.We know that $(1 + x)^3 = 1 + 3x + 3x^2 + x^3$.So,the expression becomes $((1 + x)^3)^6 = (1 + x)^{1

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(C) Given expression is $(1 + 3x + 3x^2 + x^3)^6$.We know that $(1 + x)^3 = 1 + 3x + 3x^2 + x^3$.So,the expression becomes $((1 + x)^3)^6 = (1 + x)^{18}$.For a binomial expansion $(1 + x)^n$,if $n$ is even,the middle term is given by the $(\frac{n}{2} + 1)^{th}$ term.Here,$n = 18$,which is even.Therefore,the middle term is $(\frac{18}{2} + 1)^{th} = (9 + 1)^{th} = 10^{th}$ term.

Class 11 Mathematics Binomial Theorem General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

Medium

The middle term in the expansion of $(1 + 3x + 3x^2 + x^3)^6$ is

A
$4^{th}$
B
$3^{rd}$
C
$10^{th}$
D
None of these

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Binomial Theorem

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General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

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KVPY 2009

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DifficultJEE MAIN 2026

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If the coefficients of the $r^{th}$ term and the $(r + 4)^{th}$ term are equal in the expansion of $(1 + x)^{20}$,then the value of $r$ is:

Medium

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Coefficient of $x$ in the expansion of ${\left( {{x^2} + \frac{a}{x}} \right)^5}$ is

Medium

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The numerically greatest term in the binomial expansion of $(2x - 3y)^5$ when $x = \frac{3}{2}$ and $y = \frac{2}{3}$ is

MediumTS EAMCET 2023

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The middle term in the expansion of $(1 + 3x + 3x^2 + x^3)^6$ is

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