(A) To find the sum of the coefficients in the expansion of $(x - 2y + 3z)^n$,we set $x = 1, y = 1, z = 1$.Sum $= (1 - 2 + 3)^n = 2^n$.Given $2^n = 12

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(A) To find the sum of the coefficients in the expansion of $(x - 2y + 3z)^n$,we set $x = 1, y = 1, z = 1$.Sum $= (1 - 2 + 3)^n = 2^n$.Given $2^n = 128$,we have $2^n = 2^7$,so $n = 7$.The expansion of $(1 + x)^7$ is $\sum_{r=0}^{7} {^7C_r} x^r$.The coefficients are ${^7C_0}, {^7C_1}, {^7C_2}, {^7C_3}, {^7C_4}, {^7C_5}, {^7C_6}, {^7C_7}$.The greatest coefficient is ${^7C_3} = {^7C_4} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35$.

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

Medium

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

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

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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

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