Question

Sum of the coefficients in the expansion of ${(2x+\frac{12}{n{x}^2})}^n$ is equal to $4096$. The term independent of $x$ is

• A. $860$
• B. $950$
• C. $850$
• D. $960$
• E. None of these

Answer 1

Answer: (D)

$960$

$2x+{\frac{12}{n{x}^2}}^n$

Put $x=1$

$(2+\frac{12}{n}{)}^n=4096=4^6/2^{12}$

Put $n=6\Rightarrow 2+\frac{12}{n}=4$

$\therefore n=6$

$\therefore n=6$ satisfies the condition

$\therefore$ Term independent of $x{=}^6{C}_n(2x{)}^6\times (\frac{2}{x^2}{)}^n$

$\therefore$ $x=2$, term is independent of $x$

$\therefore {=}^6{C}_2{2}^6=960$