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CUET · MATHS · PYQ PAPER 2025

If \(a , b\) and \(c\) are distinct prime numbers then the value of \(\left|\begin{array}{lll}a-b & b-c & c-a \\ b-c & c-a & a-b \\c-a & a-b & b-c\end{array}\right|\) is equal to

  1. A \(0\)
  2. B 1
  3. C \((a-b)(b-c)(c-a)\)
  4. D \((a+b)(b+c)(c+a)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(0\)

Step-by-step Solution

Detailed explanation

\(C_1 \to C_1 + C_2 + C_3\) \(\left|\begin{array}{ccc}(a-b)+(b-c)+(c-a) & b-c & c-a \\ (b-c)+(c-a)+(a-b) & c-a & a-b \\(c-a)+(a-b)+(b-c) & a-b & b-c\end{array}\right|\) \(\left|\begin{array}{lll}0 & b-c & c-a \\ 0 & c-a & a-b \\0 & a-b & b-c\end{array}\right| = 0\)