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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Determinants

NDA 2019 · Mathematics · Determinants

If x+a+b+c=0 , then what is the value of | array ccc x+a & b & c a...

If x+a+b+c=0x+a+b+c=0, then what is the value of \left|x+abcax+bcabx+c\begin{array}{ccc}x+a & b & c \\ a & x+b & c \\ a & b & x+c\end{array}\right| ?

Options

  1. A0
  2. B(a+b+c)2(a+b+c)^2
  3. Ca2+b2+c2a^2+b^2+c^2
  4. Da+b+c−2a+b+c-2

Correct answer

A. 0

Step-by-step solution

Given: x+a+b+c=0\Delta=\left|x+abcax+bcabx+c\begin{array}{ccc} x+a & b & c \\ a & x+b & c \\ a & b & x+c \end{array}\right| Replace cc, by →c1+c2+c3\rightarrow c_1+c_2+c_3\begin{array}{ll} & \left|\begin{array}{ccc} x+a+b+c & b & c \\ x+a+b+c & x+b & c \\ x+a+b+c & b & x+c \end{array}\right| \\ \because & x+a+b+c=0 \\ \therefore & \Delta=0 \end{array}
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