Question

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

• A. $7C3$
• B. $8C5$
• C. $9C3$
• D. $5C3$

Answer 1

The correct option is A $7C3$

To find the sum of coefficients, we put all variables as 1.
sum of coeffcients = $(1+3-2{)}^n$
= $2^n$
given, $2^n$ = 128
$2^n$ = $2^7$
n = 7,
expansion is $(1+x{)}^7$
The greatest binomial coefficient of any expansion is coefficient of its middle term.
for expansion of power n, if n is even, then the middle term = ((n/2) + 1)th term
if n is odd, then the middle term = ((n + 1)/2)th term or ((n + 1)/2 + 1)th term
Thus the greatest coefficient of the expansion $(1+x{)}^7$ is
$7C3\mathrm{or}7C4$