Question

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

• A. $9$
• B. $8$
• C. $7$
• D. $10$

Answer 1

The correct option is B $8$

In the expansion of $(1-x{)}^n$ it is given that, the 5th term has the largest value.
Hence
${}^n{C}_4$ should be the greatest coefficient.
This is possible, if ${}^n{C}_4$ is the middle term.
Since it is the greatest term, there has to be only one middle term, i.e, total number of term should be odd, making 'n' as an even integer.
Hence the positive integral solution for n will be
$=2\left(4\right)$
$=8$