Question

If the sum of the binomial coefficients in the expansion of ${(x^2+\frac{2}{x^3})}^n$ is $243$, the term independent of $x$ is equal to

• A. $40$
• B. $30$
• C. $20$
• D. $10$

Answer 1

The correct option is A $40$

${(x^2+\frac{2}{x^3})}^n$

Now put $x=1$

$(1+2{)}^n=243$

$3^n=243$

$n=5$

$T_{r+1}={}^5{C}_r{x}^{2(5-r)}{2}^r.x^{-3x}$ ……….$\left(1\right)$

for the term independent to x we must have

$10-2r-3r=0$

$r=2$

Put in $\left(1\right)$

$T_3={(}^5{C}_2\left)\right(2{)}^2$

$=10\times 4$

$=40$

$\therefore$ Terms independent to x$=40$.