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BITSAT 2009
Exam
BITSAT
Year
2009
Subject
Mathematics
Chapter
Sequences and Series

BITSAT 2009 · Mathematics · Sequences and Series

If in the expansion of ( ( 2^x+ (1)/(4^x))^ n, T_3=7 T_2) and sum...

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 xx is -

Options

  1. A−1/3-1 / 3
  2. B−1/2-1 / 2
  3. C1/31 / 3
  4. D1/21 / 2

Correct answer

A. −1/3-1 / 3

Step-by-step solution

nC1+nC2=36⇒n=8T3=7T2⇒(2x)3=1/23x=−1⇒x=−13\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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