CUET · MATHS · PYQ PAPER 2025
The system of equations
\(\begin{array}{l}x+y+z=4 \\x+2 y+3 z=12 \\x+3 y+\lambda z=\mu\end{array}\)
has a unique solution if
- A \(\lambda=5, \mu\) can be any real number
- B \(\lambda=5, \mu \neq 20\)
- C \(\lambda \neq 5, \mu\) can be any real number
- D \(\lambda=5, \mu=20\)
Answer & Solution
Correct Answer
(C) \(\lambda \neq 5, \mu\) can be any real number
Step-by-step Solution
Detailed explanation
The system has a unique solution if the determinant of the coefficient matrix is non-zero. \(\begin{vmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & \lambda \end{vmatrix} = 1(2\lambda - 9) - 1(\lambda - 3) + 1(3 - 2)\) \(= 2\lambda - 9 - \lambda + 3 + 1\) \(= \lambda - 5\) For a…
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