CUET · MATHS · PYQ PAPER 2025
If the system of equation
\(x-y+z=4\)
\(x-2 y-2 z=9\)
\(2 x+y+\lambda z=1\)
has a unique solution, then
- A \(\lambda \geq 11\)
- B \(\lambda=11\)
- C \(\lambda \neq 11\)
- D \(\lambda \leq 11\)
Answer & Solution
Correct Answer
(C) \(\lambda \neq 11\)
Step-by-step Solution
Detailed explanation
\(D = \begin{vmatrix} 1 & -1 & 1 \\ 1 & -2 & -2 \\ 2 & 1 & \lambda \end{vmatrix}\) \(D = 1(-2\lambda - (-2)) - (-1)(\lambda - (-4)) + 1(1 - (-4))\) \(D = -2\lambda + 2 + \lambda + 4 + 5\) \(D = -\lambda + 11\) For a unique solution, \(D \neq 0\) \(-\lambda + 11 \neq 0\)…
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