Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

JEE Main 202623 JanuaryEvening Shift

Exam: JEE Main
Year: 2026
Date: 23 January
Shift: Evening Shift
Subject: Mathematics
Chapter: Determinants

JEE Main 2026 · 23 January · Evening Shift · Mathematics · Determinants

The system of linear equations x+y+z=6 2 x+5 y+a z=36 x+2 y+3 z=b...

The system of linear equations

x+y+z=6

2 x+5 y+a z=36

x+2 y+3 z=b

has

Options

Aunique solution for $a=8$ and $b=16$
Binfinitely many solutions for $a=8$ and $b=16$
Cunique solution for $a=8$ and $b=14$
Dinfinitely many solutions for $a=8$ and $b=14$

Correct answer

D. infinitely many solutions for $a=8$ and $b=14$

Step-by-step solution

Coefficient matrix determinant:

\Delta = 1(15-2a) - 1(6-a) + 1(4-5) = 8 - a

.
For

a = 8

,

\Delta = 0

, so unique solution is not possible.
With

a = 8

:

R_2 - 2R_1

gives

3y + 6z = 24 \Rightarrow y + 2z = 8

.

R_3 - R_1

gives

y + 2z = b - 6

.
For consistency:

b - 6 = 8 \Rightarrow b = 14

.
When

a = 8, b = 14

: the system has infinitely many solutions.

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 2026 The sum of all possible values of θ ∈ [0, 2π] , for which the system of equations : x 3θ… JEE Main 2026 If f: N arrow Z is defined by f(n) = vmatrix n & -1 & -5 -2n^2 & 3(2k+1) & 2k+1 -3n^3 &… JEE Main 2026 Consider the system of linear equations in x, y, z : x + 2y + tz = 0 , 6x + y + 5tz = 0… JEE Main 2026 If the system of equations: x+y+z=5 x+2y+3z=9 x+3y+λ z=μ has infinitely many solutions… JEE Main 2026 If the system of equations x + 5y + 6z = 4 , 2x + 3y + 4z = 7 , x + 6y + az = b has… JEE Main 2026 Let α, β ∈ ℝ be such that the system of linear equations x + 2y + z = 5 2x + y + α z = 5… JEE Main 2026 Among the statements : I: If | array ccc 1 & α & β α & 1 & γ β & γ & 1 array |=| array… JEE Main 2026 Let n be the number obtained on rolling a fair die. If the probability that the system… JEE Main 2026 If 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 2026 Let 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 2025 Let 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 2025 If y(x)=| array ccc x & x & x+ x+1 27 & 28 & 27 1 & 1 & 1 array |, x ∈ ℝ , then (d^2… JEE Main 2025 If 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 2025 If 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 Let α, β(α ≠ β) be the values of m , for which the equations x+y+z=1 ; x+2 y+4 z=m and… JEE Main 2025 Full Determinants list Determinants JEE Maths PYQs JEE Mathematics PYQs All JEE Main PYQs