Q174 / 270 · NDA 2022 (Phase 2) · Mathematics
Paragraph:
Consider the binomial expansion of $(p+q x)^9$ :Question:
Under what condition the coefficients of $x^2$ and $x^4$ are equal?
- A$p: q=7: 2$
- Correct answerB$p^2: q=7: 2$
- C$p: q=2: 7$
- D$p^2: q^2=2: 7$
Solution
coefficient of $x^2=$ coefficient of $x^4$
$\begin{aligned}
& { }^9 C_2 p^7 q^2={ }^9 C_4 p^5 q^4 \\
& \frac{9.8}{2.1} p^2=\frac{9.8 .7 .6}{4.3 .2 .1} q^2 \\
& \frac{p^2}{q^2}=\frac{7}{2}
\end{aligned}$
Hence, the correct answer is option: 'B'.