If sum of coefficients in expansion of {(x - 2y + 3z)^n} is 128 then greatest coefficient in expansi

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7.Binomial Theorem

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

A

$35$

B

$20$

C

$10$

D

None of these

Solution

(a) Sum of the coefficient in the expansion

${(x – 2y + 3z)^n}$is ${(1 – 2 + 3)^2} = {2^n}$

${2^n} = 128 \Rightarrow n = 7$

Therefore, greatest coefficient in the expansion of ${(1 + x)^7}$is $^7{C_3}$or

$^7{C_4}$because both are equal to 35.

Standard 11

Mathematics

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