Q6 / 120 · NDA 2024 (Phase 2) · Mathematics

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

  • A
    $5$
  • B
    $6$
  • Correct answer
    C
    $7$
  • D
    $8$

Solution

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

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

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