Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 201815 AprilEvening ShiftOnline
Exam
JEE Main
Year
2018
Date
15 April
Shift
Evening Shift
Mode
Online
Subject
Mathematics
Chapter
Determinants

JEE Main 2018 · 15 April · Evening Shift · Online · Mathematics · Determinants

If the system of linear equations aligned &x+a y+z=3 &x+2 y+2 z=6...

If the system of linear equations x+ay+z=3x+2y+2z=6x+5y+3z=b\begin{aligned} &x+a y+z=3 \\ &x+2 y+2 z=6 \\ &x+5 y+3 z=b \end{aligned} has no solution, then

Options

  1. Aa=1,b≠9a=1, b \neq 9
  2. Ba≠−1,b=9a \neq-1, b=9
  3. Ca=−1,b=9a=-1, b=9
  4. Da=−1,b≠9a=-1, b \neq 9

Correct answer

D. a=−1,b≠9a=-1, b \neq 9

Step-by-step solution

As the system of equations has no solution then Δ\Delta should be zero and at least one of Δ1\Delta_1, Δ2\Delta_2 and Δ3\Delta_3 should not be zero. ∴Δ=∣1a1122153∣=0⇒−a−1=0⇒a=−1Δ2=∣1311621b3∣≠0⇒b≠9\begin{aligned}&\therefore \Delta=\left|\begin{array}{lll}1 & a & 1 \\ 1 & 2 & 2 \\ 1 & 5 & 3 \end{array}\right|=0 \\ &\Rightarrow-a-1=0 \Rightarrow a=-1 \\ &\Delta_2=\left|\begin{array}{lll}1 & 3 & 1 \\ 1 & 6 & 2 \\ 1 & b & 3 \end{array}\right| ≠ 0 \\ &\Rightarrow b ≠ 9 \end{aligned}
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