(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

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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

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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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