Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Black Book Advanced Problems in MathematicsMathematicsDeterminants

The system of equations kx + (k+1)y + (k-1)z = 0 (k+1) x + ky + (k+2)z = 0 (k-1)x + (k+2) y + kz = 0 has a nontrivial solution for:

Options

  1. AExactly three real values of k.
  2. BExactly two real values of k.
  3. CExactly one real value of k.
  4. DInfinite number of values of k.

Correct answer

C. Exactly one real value of k.

Step-by-step solution

Open this question in the Quantrex Academy app for the full interactive solution, figures and similar PYQs.

Practice Determinants on Quantrex Academy →

More from Determinants

If the system of linear equations: x+y+z=6 , x+2y+5z=10 , 2x+3y+ z= has infinitely many solutions, then the value of + equals: 2026The sum of all possible values of [0, 2 ] , for which the system of equations : x 3 - 8y - 12z = 0 x 2 + 3y + 3z = 0 x + y + 3z = 0 has a non-trivial solution, is equal to : 2026If f: N Z is defined by f(n) = vmatrix n & -1 & -5 -2n^2 & 3(2k+1) & 2k+1 -3n^3 & 3k(2k+1) & 3k(k+2)+1 vmatrix , k N , and _ n=1 ^ k f(n) = 98 , then k is equal to : 2026Consider the system of linear equations in x, y, z : x + 2y + tz = 0 , 6x + y + 5tz = 0 , 3x + t^2 y + f(t) z = 0 , where f: R R is a differentiable function. If this system has in 2026If the system of equations: x+y+z=5 x+2y+3z=9 x+3y+ z= has infinitely many solutions, then the value of + is: 2026If the system of equations x + 5y + 6z = 4 , 2x + 3y + 4z = 7 , x + 6y + az = b has infinitely many solutions, then the point (a, b) lies on the line 2026Let , R be such that the system of linear equations x + 2y + z = 5 2x + y + z = 5 8x + 4y + z = 18 has no solution. Then is equal to : 2026The system of linear equations x+y+z=6 2 x+5 y+a z=36 x+2 y+3 z=b has 2026 Full Determinants list All Black Book Advanced Problems in Mathematics PYQs