Q173 / 270 · NDA 2022 (Phase 2) · Mathematics

Paragraph: Consider the binomial expansion of $(p+q x)^9$ :Question: What is the ratio of the coefficients of middle terms in the expansion (when expanded in ascending powers of $x$ )?

  • A
    $p q$
  • Correct answer
    B
    $\frac{p}{q}$
  • C
    $\frac{4 p}{5 q}$
  • D
    $\frac{1}{(p q)}$

Solution

Middle terms $\begin{aligned} & T_5=T_{4+1}={ }^9 C_4 p^5 q^4 x^4 \\ & T_6=T_{5+1}={ }^9 C_5 p^4 q^5 x^5 \\ & \text { Ratio of coefficients }=\frac{{ }^9 C_5 p^5 q^4}{{ }^9 C_4 p^4 q^5}=\frac{p}{q} \end{aligned}$

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

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