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JEE Main20258 Apr 2025Evening ShiftMathematicsMatricesActual

Let A= [ array ccc 2 & 2+p & 2+p+q 4 & 6+2 p & 8+3 p+2 q 6 & 12+3 p & 20+6 p+3 q array ] . If det ( adj ( adj (3 ~A )))=2^ m 3^ n , m , n N , then m + n is equal to

Options

  1. A22
  2. B24
  3. C26
  4. D20

Correct answer

B. 24

Step-by-step solution

|A|= | array ccc 2 & 2+p & 2+p+q 4 & 6+2 p & 8+3 p+2 q 6 & 12+3 p & 20+6 p+3 q array | C ₃ C ₃- C ₂- C ₁ q 2 Then C ₃ C ₂- C ₁ X (1+ p 2 ) aligned & | A |= | array ccc 2 & 0 & 0 4 & 2 & 2+ p 6 & 6 & 8+3 p array | & | A |=2(16+6 p -12-6 p )=8=2^3 & | adj ( adj (3 ~A ))|=|3 ~A |^ (3-1)^2 =|3 ~A |^4 & = (3^3| ~A | )^4= (3^3 2^3 )^4=2¹² 3¹² & ~m + n =24 aligned

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