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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Determinants

NDA 2018 · Mathematics · Determinants

Which one of the following factors does the expansions of the...

Which one of the following factors does the expansions of the determinant \left(xy3x25y39x310y327\begin{array}{ccc}x & y & 3 \\ x^2 & 5 y^3 & 9 \\ x^3 & 10 y^3 & 27\end{array}\right) contain?

Options

  1. Ax−3\mathrm{x}-3
  2. Bx−yx-y
  3. CY−3\mathrm{Y}-3
  4. Dx−3yx-3 y

Correct answer

A. x−3\mathrm{x}-3

Step-by-step solution

On Applying \begin{array}{r} \mathrm{C}_1 \rightarrow \mathrm{C}_1-\mathrm{C}_3 \\ \qquad\left|\begin{array}{ccc} x-3 & y & 3 \\ x^2-9 & 5 y^3 & 9 \\ x^3-27 & 10 y^5 & 27 \end{array}\right| \\ (x-3)\left|1y3x+35y39x2+9−3x10y527\begin{array}{ccc} 1 & y & 3 \\ x+3 & 5 y^3 & 9 \\ x^2+9-3 x & 10 y^5 & 27 \end{array}\right| \end{array}
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