If in the expansion of $\left(2^x+\frac{1}{4^x}\right)^n, T_3=7 T_2$ and sum of the binomial coefficients of second and third terms is 36 , then the value of $x$ is -

Question

If in the expansion of $\left(2^x+\frac{1}{4^x}\right)^n, T_3=7 T_2$ and sum of the binomial coefficients of second and third terms is 36 , then the value of $x$ is -, $-1 / 3$, $-1 / 2$, $1 / 3$, $1 / 2$

MARKS App · Accepted Answer

$\begin{aligned} & { }^n C_1+{ }^n C_2=36 \Rightarrow n=8 \ & T_3=7 \mathrm{~T}_2 \Rightarrow\left(2^{\mathrm{x}}\right)^3=1 / 2 \ & 3 \mathrm{x}=-1 \Rightarrow \mathrm{x}=-\frac{1}{3} \end{aligned}$

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