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Jee Main 2025Medium JEE math MCQ

\((\lambda - 1)x + (\lambda - 4)y + \lambda z = 5 \) If the system of equations \( \lambda x + (\lambda - 1)y + (\lambda - 4)z = 7 \) has infinitely many solutions, then \( \lambda^2 + \lambda \) is equal to \begin{align*}
  1. A. \ 6 & & \quad
  2. B. \ 10 \\
  3. C. \ 20 & & \quad
  4. D. \ 12 \end{align*}

Solution

The correct option is **D**. (D. \ 12 \end{align*})

MATH

mediumPYQ Reworded
Question
Read carefully, then pick the best option.
(λ1)x+(λ4)y+λz=5(\lambda - 1)x + (\lambda - 4)y + \lambda z = 5 If the system of equations λx+(λ1)y+(λ4)z=7 \lambda x + (\lambda - 1)y + (\lambda - 4)z = 7 has infinitely many solutions, then λ2+λ \lambda^2 + \lambda is equal to \begin{align*}
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep