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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2022 · Mathematics · Binomial Theorem

Paragraph: Consider the binomial expansion of (p+q x)^9 : Question:...

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

Options

  1. Apqp q
  2. Bpq\frac{p}{q}
  3. C4p5q\frac{4 p}{5 q}
  4. D1(pq)\frac{1}{(p q)}

Correct answer

B. pq\frac{p}{q}

Step-by-step solution

Middle terms T5=T4+1=9C4p5q4x4T6=T5+1=9C5p4q5x5 Ratio of coefficients =9C5p5q49C4p4q5=pq\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}
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