Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202127 Aug 2021Evening ShiftMathematicsDeterminantsActual

Let [ λ ] be the greatest integer less than or equal to λ . The set of all values of λ for which the system of linear equations x + y + z = 4 , 3 x + 2 y + 5 z = 3 , 9 x + 4 y + ( 28 + [ λ ] ) z = [ λ ] has a solution is:

Options

  1. AR
  2. B( - ∞ , - 9 ) ∪ [ - 8 , ∞ )
  3. C( - ∞ , - 9 ) ∪ ( - 9 , ∞ )
  4. D[ - 9 , - 8 )

Correct answer

A. R

Step-by-step solution

Given, the system of linear equations, x + y + z = 4   . . . . . . . . . . . . . . . . . . . . . . . . i 3 x + 2 y + 5 z = 3 . . . . . . . . . . . . . . . . i i 9 x + 4 y + ( 28 + [ λ ] ] z = [ λ ] . . . . . . . . . . . . . . . . . . . . . i i i D = 1 1 1 3 2 5 9 4 28 + [ λ ] = 1 56 + 2 λ - 20 - 1 84 + 3 λ - 45 + 1 12 - 18   D = − ( [ λ ] + 9 ) If D = - [ λ ] + 9 ≠ 0 then unique solution If D = - [ λ ] + 9 = 0 then D 1 = D 2 = D 3 = 0 infinite 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+ 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 JEE Main PYQs