Question

The sum of the coefficients of the binomial expansion of ${(\frac{1}{x}+2x)}^n$ is equal to 6561. The constant term in the expansion is

• A.
• B.
• C.
• D. \(None~of~these

Answer 1

The correct option is B

The sum of all the coefficients in an expansion is obtained by putting x = 1 in the expression.
$\therefore {(\frac{1}{1}+2.1)}^n=6561\therefore 3^n=3^8\therefore n=8In{(\frac{1}{x}+2x)}^8,t_{r+1}{=}^8{C}_r{\left(\frac{1}{x}\right)}^{8-r}.(2x{)}^{r}Thisisaconstantif8-2r=0,i.e.,r=4\therefore Theconstantterm=t_5{=}^8{C}_4{.2}^4$