Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main20249 Apr 2024Morning ShiftMathematicsDeterminantsActual

Let , R . If the system of equations aligned & 3 x+5 y+ z=3 & 7 x+11 y-9 z=2 & 97 x+155 y-189 z= aligned has infinitely many solutions, then +2 is equal to :

Options

  1. A24
  2. B25
  3. C22
  4. D27

Correct answer

B. 25

Step-by-step solution

array l 3 x+5 y+ z=3 7 x+11 y-9 z=2 97 x+155 y-189 z= 93 x+155 y+31 z=93 97 x+155 y-189 z= - + + - -4 x+(31 +189) z=93- 1085 x+1705 y-1395 z=310 1067 x+1705 y-2079 z=11 - + - 18 x+684 z=310-11 array aligned & -36 x+9(31 +189) z=9(93- ) & 36 x+1368 z=2(310-11 ) & (279 +3069) z=1457-31 aligned for infinite solutions - aligned & = -3069 279 = -341 31 & = 1457 31 aligned +2 = 1457-682 31 = 775 31 =25

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