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7.Binomial Theorem
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
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