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CUET · MATHS · PYQ PAPER 2023

The value of the determinant \(\left|\begin{array}{lll}a-b & b+c & a \\b-c & c+a & b \\c-a & a+b & c\end{array}\right| \text { is : }\)

  1. A \(a^3+b^3+c^3\)
  2. B \(-3 b c\)
  3. C \(a^3+b^3+c^3-3 a b c\)
  4. D \(-(a+b+c)(b-c)(a-b)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(a^3+b^3+c^3-3 a b c\)

Step-by-step Solution

Detailed explanation

\( \left|\begin{array}{lll}a-b & b+c & a \\b-c & c+a & b \\c-a & a+b & c\end{array}\right| \) \( R_1 \rightarrow R_1 + R_2 + R_3 \) \( = \left|\begin{array}{ccc} (a-b)+(b-c)+(c-a) & (b+c)+(c+a)+(a+b) & a+b+c \\ b-c & c+a & b \\ c-a & a+b & c\end{array}\right| \)…