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JEE Main 202621 JanuaryEvening Shift
Exam
JEE Main
Year
2026
Date
21 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Determinants

JEE Main 2026 · 21 January · Evening Shift · Mathematics · Determinants

If the system of equations 3 x+y+4 z=3 2 x+α y-z=-3 x+2 y+z=4 has...

If the system of equations
3x+y+4z=33 x+y+4 z=3
2x+αy−z=−32 x+\alpha y-z=-3
x+2y+z=4x+2 y+z=4
has no solution, then the value of α\alpha is equal to :

Options

  1. A1919
  2. B4
  3. C13
  4. D23

Correct answer

A. 1919

Step-by-step solution

For no solution Δ=0\Delta = 0
∣3142α−1121∣=0\begin{vmatrix} 3 & 1 & 4 \\ 2 & \alpha & -1 \\ 1 & 2 & 1 \end{vmatrix} = 0
⇒3(α+2)+1(−1−2)+4(4−α)=0\Rightarrow 3(\alpha + 2) + 1(-1 - 2) + 4(4 - \alpha) = 0
⇒19−α=0⇒α=19\Rightarrow 19 - \alpha = 0 \Rightarrow \boxed{\alpha = 19}
& for α=19\alpha = 19
Δx=∣314−319−1421∣=3(21)+1(−1)+4(−82)\Delta_x = \begin{vmatrix} 3 & 1 & 4 \\ -3 & 19 & -1 \\ 4 & 2 & 1 \end{vmatrix} = 3(21) + 1(-1) + 4(-82)
≠0\neq 0
∴\therefore no solution for α=19\alpha = 19
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