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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2024 · Mathematics · Binomial Theorem

In the expansion of (1+x)^p(1+x)^q , if the coefficient of x^3 is...

In the expansion of (1+x)p(1+x)q(1+x)^p(1+x)^q, if the coefficient of x3x^3 is 35 , then what is the value of (p+q)(p+q) ?

Options

  1. A55
  2. B66
  3. C77
  4. D88

Correct answer

C. 77

Step-by-step solution

Here, (1+x)p(1+x)q=(1+x)p+q(1+\mathrm{x})^{\mathrm{p}}(1+\mathrm{x})^{\mathrm{q}}=(1+\mathrm{x})^{\mathrm{p}+\mathrm{q}} Given, Coeff. of x3x^3 in the expansion of (1+x)p+q=35(1+x)^{p+q}=35⇒(p+q)C3=35=7C3⇒p+q=7\begin{aligned} & \Rightarrow \quad(p+q) C_3=35={ }^7 C_3 \\ & \Rightarrow p+q=7 \end{aligned}$$ (on comparison)
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