Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 2003
Exam
JEE Main
Year
2003
Subject
Mathematics
Chapter
Determinants

JEE Main 2003 · Mathematics · Determinants

If 1, ω, ω^2 are the cube roots of unity, then Δ=| array ccc 1 &...

If 1,ω,ω21, \omega, \omega^2 are the cube roots of unity, then \Delta=\left|1ωnω2nωnω2n1ω2n1ωn\begin{array}{ccc}1 & \omega^n & \omega^{2 n} \\ \omega^n & \omega^{2 n} & 1 \\ \omega^{2 n} & 1 & \omega^n\end{array}\right| is equal to

Options

  1. Aω2\omega^2
  2. B0
  3. C1
  4. Dω\omega

Correct answer

B. 0

Step-by-step solution

Applying R1→R1+R2+R3\mathrm{R}_1 \rightarrow \mathrm{R}_1+\mathrm{R}_2+\mathrm{R}_3 As, 1+ωn+ω2n=0;∴Δ=01+\omega^{\mathrm{n}}+\omega^{2 \mathrm{n}}=0 ; \quad \therefore \Delta=0
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