Question

In the expansion of $(x+y{)}^n,$ if the binomial coefficient of the third term is greater by 9 than that of the second term, then the sum of the binomial coefficients of the terms occupying the odd places is :

• A. $2^9$
• B. $2^6$
• C. $2^5$
• D. $2^8$

Answer 1

Answer: (C)

$2^5$

It is given that
$T_3=T_2+9$
${}^n{C}_2={}^n{C}_1+9$
$\frac{n(n-1)}{2}=n+9$
$n^2-n=2n+18$
$n^2-3n-18=0$
$(n+3)(n-6)=0$
Since $nϵN$
$\Rightarrow n=6$
Sum of the binomial coefficients of the terms occupying the odd places
$=2^{n-1}$
$=2^{6-1}$
$=2^5$