Question

If the coefficient of the 5th term is the numerically the greatest coefficient in the expansion of ${(1-x)}^n$, then the positive integral value of $n$ is

• A. $10$
• B. $9$
• C. $8$
• D. $7$

Answer 1

Answer: (C)

$8$

We know that, the coefficient of the middle term is the numerically greatest coefficient in the expansion of ${(1+x)}^n$ or ${(1+x)}^n$ and its value is ${{}^{n}C}_{n/\alpha }$ or $\frac{{{}^{n}C}_{n+1}}{2}=\frac{{{}^{n}C}_{n-1}}{2}$ according as $n$ is even or odd.
It is given that the coefficient of the 5th term is the greatest. Therefore, 5th term is the middle term. Thus, there are $9$ terms. Hence, $n=8$.