Q52 / 125 · BITSAT 2009 · Mathematics

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 -

Correct answer
A
\(-1 / 3\)
B
\(-1 / 2\)
C
\(1 / 3\)
D
\(1 / 2\)

Solution

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

Hence, the correct answer is option: 'A'.

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