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JEE Main20257 Apr 2025Morning ShiftMathematicsDeterminantsActual

Let the system of equations : aligned & 2 x+3 y+5 z=9 & 7 x+3 y-2 z=8 & 12 x+3 y-(4+ ) z=16- aligned have infinitely many solutions. Then the radius of the circle centred at ( , ) and touching the line 4 x=3 y is

Options

  1. A17 5
  2. B7 5
  3. C7
  4. D21 5

Correct answer

B. 7 5

Step-by-step solution

aligned & | array ccc 2 & 3 & 5 7 & 3 & -2 12 & 3 & -( +4) array |=0 & 12(-21)-3(-39)-( +4)(-15)=0 & -252+117+15(1+4)=0 & 15 +177-252=0 & 15 -75=0 =5 & | array ccc 9 & 3 & 5 8 & 3 & -2 16- & 3 & -9 array |=0 | array ccc 1 & 0 & 7 -8 & 0 & 7 16- & 3 & -9 array |=0 & 7-7( -8)=0 1-( -8)=0 =9 & centre of circle (5,9) & radius = length of from centre (5, 9)= & | 20-27 5 |= 7 5 aligned

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