Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20204 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
4 September
Shift
Evening Shift
Subject
Mathematics
Chapter
Determinants

JEE Main 2020 · 4 September · Evening Shift · Mathematics · Determinants

If the system of equations x + y + z = 2 2x + 4y - z = 6 3x + 2y +...

If the system of equations

x+y+z=2x + y + z = 2
2x+4y−z=62x + 4y - z = 6
3x+2y+\lambdaz=μ3x + 2y + \lambdaz = \mu

has infinitely many solutions, then :

Options

  1. Aλ+2μ=14\lambda + 2\mu = 14
  2. B2λ−μ=52\lambda - \mu = 5
  3. Cλ−2μ=−5\lambda - 2\mu = - 5
  4. D2λ+μ=142\lambda + \mu = 14

Correct answer

D. 2λ+μ=142\lambda + \mu = 14

Step-by-step solution

For infinitely many solutions, all determinants should be zero.

D = \left|\begin{cases}1 & 1 & 1 \\ 2 & 4 & - 1 \\ 3 & 2 & \lambda\end{cases}\right| = 0 ⇒ \lambda = \dfrac{9}{2}

{D}_{3} = \left|\begin{cases}1 & 1 & 2 \\ 2 & 4 & 6 \\ 3 & 2 & \mu\end{cases}\right| = 0 ⇒ \mu = 5

Now check each option

Practice Determinants on Quantrex Academy →

More from Determinants

If the system of linear equations: x+y+z=6 , x+2y+5z=10 , 2x+3y+λ z=μ has infinitely many… JEE Main 2026The sum of all possible values of θ ∈ [0, 2π] , for which the system of equations : x 3θ… JEE Main 2026If f: N arrow Z is defined by f(n) = vmatrix n & -1 & -5 -2n^2 & 3(2k+1) & 2k+1 -3n^3 &… JEE Main 2026Consider the system of linear equations in x, y, z : x + 2y + tz = 0 , 6x + y + 5tz = 0… JEE Main 2026If the system of equations: x+y+z=5 x+2y+3z=9 x+3y+λ z=μ has infinitely many solutions… JEE Main 2026If the system of equations x + 5y + 6z = 4 , 2x + 3y + 4z = 7 , x + 6y + az = b has… JEE Main 2026Let α, β ∈ ℝ be such that the system of linear equations x + 2y + z = 5 2x + y + α z = 5… JEE Main 2026The system of linear equations x+y+z=6 2 x+5 y+a z=36 x+2 y+3 z=b has JEE Main 2026Among the statements : I: If | array ccc 1 & α & β α & 1 & γ β & γ & 1 array |=| array… JEE Main 2026Let n be the number obtained on rolling a fair die. If the probability that the system… JEE Main 2026If the system of equations 3 x+y+4 z=3 2 x+α y-z=-3 x+2 y+z=4 has no solution, then the… JEE Main 2026Let the system of equations aligned & x+5 y-z=1 & 4 x+3 y-3 z=7 & 24 x+y+λ z=μ aligned λ… JEE Main 2025Let the system of equations : aligned & 2 x+3 y+5 z=9 & 7 x+3 y-2 z=8 & 12 x+3 y-(4+λ)… JEE Main 2025If y(x)=| array ccc x & x & x+ x+1 27 & 28 & 27 1 & 1 & 1 array |, x ∈ ℝ , then (d^2… JEE Main 2025If the system of equation aligned & 2 x+λ y+3 z=5 & 3 x+2 y-z=7 & 4 x+5 y+μ z=9 aligned… JEE Main 2025If the system of linear equations aligned & 3 x+y+β z=3 & 2 x+α y-z=-3 & x+2 y+z=4… JEE Main 2025 Full Determinants list Determinants JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs