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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 value of qq if the coefficients of x3x^3 and x6x^6 are equal ?

Options

  1. App
  2. B9p9 p
  3. C1p\frac{1}{p}
  4. Dp2p^2

Correct answer

A. pp

Step-by-step solution

Given expansion is (p+qx)9Tr+1=9Cr⁡p9−r(qx)r=9Cr⁡ppq−rqrxr∵(p+q x)^9T^{\mathrm{r}+1}={ }^9 \operatorname{Cr} p^{9-\mathrm{r}}(q x)^{\mathrm{r}}={ }^9 \operatorname{Cr} p p^{\mathrm{q}-\mathrm{r}} q^{\mathrm{r}} x^{\mathrm{r}}\because \quad coefficient of x3=x^3= coefficient x6x^69C3p6q3=9C6p3q6⇒p3=q3⇒p=q\begin{aligned} & { }^9 C_3 p^6 q^3={ }^9 C_6 p^3 q^6 \\ & \Rightarrow p^3=q^3 \\ & \Rightarrow p=q \end{aligned}$$
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