First slide

Binomial theorem for positive integral Index

Question

$If the sum of the coefficients in the expansion of (x - 2 y + 3 z)^{n}, n \in ℕ is 128, then the$ $greatest coefficient in the expansion of (1 + x)^{n} is$

Moderate

A

35
B

20
C

10
D

15

Solution

Sum of the coefficients in the expansion
$\begin{array}{l} (x - 2 y + 3 z)^{n} is (1 - 2 + 3)^{n} = 2^{n} (∵ Put x = y = z = 1) \\ i.e. 2^{n} = 128 \Rightarrow n = 7 \end{array}$
$\begin{array}{l} therefore, greatest coefficient in the expansion of (1 + x)^{7} {is}^{7} C_{3} {or}^{7} C_{4} \\ \Rightarrow^{7} C_{3} =^{7} C_{4} = 35 \end{array}$

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