First slide

Binomial theorem for positive integral Index

Question

If sum of the coefficient in the binomial expansion of ${(1 + 2 x)}^{n}$ is $6561,$ then coefficient of the fourth term
is :

Moderate

A

442
B

446
C

448
D

472

Solution

Sum of the coefficients
$\begin{array}{l} = (1 + 2)^{n} = 3^{n} = 3^{8} \Rightarrow n = 8 . \\ T_{4} =^{8} C_{3} (2 x)^{3} =^{8} C_{3} 2^{3} x^{3} \end{array}$
Thus, coefficient of fourth term is 448.

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