If sum of coefficients in expansion of (x - 2y + 3 z)^n, n ∈ N is 128 then greatest coefficie nt i

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7.Binomial Theorem

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If the sum of the coefficients in the expansion of $(x - 2y + 3 z)^n,$ $n \in N$ is $128$ then the greatest coefficie nt in the exp ansion of $(1 + x)^n$ is

A

$35$

B

$20$

C

$10$

D

$15$

Solution

Sum of the coefficient in the expansion

${\left( {x – 2{\rm{ }}y + 3{\rm{ }}z} \right)^n}$ is $(1-2+3)^{n}=2^{n}$

i.e. $2^{n}=128 \Rightarrow n=7$

therefore, greatest coefficient in the expansion of $(1+\mathrm{x})^{7}$ is $^{7} \mathrm{C}_{3}$ ór $^{7} \mathrm{C}_{4}$

$^{7} \mathrm{C}_{3}=^{7} \mathrm{C}_{4}=35$

Standard 11

Mathematics

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