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JEE Main20245 Apr 2024Evening ShiftMathematicsDeterminantsActual

The values of m, n , for which the system of equations aligned & x+y+z=4, & 2 x+5 y+5 z=17, & x+2 y+ m z= n aligned has infinitely many solutions, satisfy the equation:

Options

  1. Am^2+n^2-m n=39
  2. Bm^2+n^2-m-n=46
  3. Cm^2+n^2+m+n=64
  4. Dm^2+n^2+m n=68

Correct answer

A. m^2+n^2-m n=39

Step-by-step solution

aligned & D = | array lll 1 & 1 & 1 2 & 5 & 5 1 & 2 & ~m array |=0 m =2 & D ₃= | array ccc 1 & 1 & 4 2 & 5 & 17 1 & 2 & n array |=0 n =7 aligned

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