(C) The general term in the expansion of $(a + b)^n$ is given by $T_{r+1} = {}^nC_r a^{n-r} b^r$.For the $4^{th}$ term,$r = 3$,so $T_4 = {}^nC_3 a^{n-

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(C) The general term in the expansion of $(a + b)^n$ is given by $T_{r+1} = {}^nC_r a^{n-r} b^r$.For the $4^{th}$ term,$r = 3$,so $T_4 = {}^nC_3 a^{n-3} b^3$.The coefficient of the $4^{th}$ term is ${}^nC_3 = 56$.Using the formula ${}^nC_3 = \frac{n(n-1)(n-2)}{3 \times 2 \times 1} = 56$.$n(n-1)(n-2) = 56 \times 6$.$n(n-1)(n-2) = 336$.We look for three consecutive integers whose product is $336$.$8 \times 7 \times 6 = 336$.Therefore,$n = 8$.

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

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If the coefficient of the $4^{th}$ term in the expansion of $(a + b)^n$ is $56$,then $n$ is

A
$12$
B
$10$
C
$8$
D
$6$

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

If the coefficient of $x$ in the expansion of $\left(x^2+\frac{k}{x}\right)^5$ is $270$,then $k$ is equal to

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If $p$ and $q$ are real numbers such that the $7^{\text{th}}$ term in the expansion of $\left(\frac{5}{p^3} - \frac{3q}{7}\right)^8$ is $700$,then $49p^2 =$ (in $q^2$)

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The coefficient of $x^2$ in the expansion of $(2x^2 + \frac{1}{x})^{10}, x \neq 0$, is:

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If the coefficient of the $4^{th}$ term in the expansion of $(a + b)^n$ is $56$,then $n$ is

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