Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas JEE Main2020MathematicsDeterminantsPractice

If the system of equations x - 2 y + 5 z = 3, 2 x - y + z = 1, and 11 x - 7 y + p z = q has infinitely many solutions, then

Options

  1. Ap + q = 2
  2. Bp + q = 10
  3. Cp - q = 2
  4. Dp - q = 5

Correct answer

C. p - q = 2

Step-by-step solution

⇒ for infinite solution D = 0 , D 1 = 0 , D 2 = 0 , D 3 = 0 D = 1 - 2 5 2 - 1 1 11 - 7 p = 0 ⇒ - p + 7 + 2 2 p - 11 + 5 - 14 + 11 = 0 ⇒ - p + 7 + 4 p - 22 - 15 = 0 ⇒ 3 p - 30 = 0 ⇒ p = 1 0 D 1 = 3 - 2 5 1 - 1 1 q - 7 10 = 0 ⇒ 3 - 10 + 7 + 2 10 - q + 5 - 7 + q = 0 ⇒ - 9 + 20 - 2 q - 35 + 5 q = 0 ⇒ - 24 + 3 q = 0 q = 8 D 2 = 1 3 5 2 1 1 11 q 10 = 0 ⇒ 10 - q - 3 9 + 5 2 q - 11 ⇒ 10 + 9 q - 27 - 55 = 0 ⇒ q = 8 D 3 = 1 - 2 3 2 - 1 1 11 - 7 q = 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+ 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 NTA Abhyas JEE Main PYQs