Q171 / 270 · NDA 2016 (Phase 2) · Mathematics

Paragraph: Let $a x^3+b x^2+c x+d=\left|\begin{array}{lcc}x+1 & 2 x & 3 x \\ 2 x+3 & x+1 & x \\ 2-x & 3 x+4 & 5 x-1\end{array}\right|$ thenQuestion: What is the value of $c$ ?

  • A
    $-1$
  • B
    $34$
  • Correct answer
    C
    $35$
  • D
    $50$

Solution

$\begin{aligned} & \mathrm{ax}^3+\mathrm{bx}^2+\mathrm{cx}+\mathrm{d} \\ & \begin{aligned}=(\mathrm{x}+1)[(x+1)(5 x-1)-\mathrm{x}(3 \mathrm{x}+4)]-2 \mathrm{x}[(2 \mathrm{x}+3)(5 \mathrm{x}-1) \\ \quad-\mathrm{x}(2-\mathrm{x})]+3 \mathrm{x}[(2 \mathrm{x}+3)(3 x+4)-(2-x)(x+1)]\end{aligned}\end{aligned}$ $\begin{aligned} & \Rightarrow \quad a x^3+b x^2+c x+d=x^3+28 x^2+35 x-1 \\ & \Rightarrow \quad c=35\end{aligned}$

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

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