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JEE Main20246 Apr 2024Morning ShiftMathematicsDeterminantsActual

For , R and a natural number n , let A_r= | array ccc r & 1 & n^2 2 + 2 r & 2 & n^2- 3 r-2 & 3 & n(3 n-1) 2 array | . Then

Options

  1. A0
  2. B4 +2
  3. C2 +4
  4. D2 n

Correct answer

B. 4 +2

Step-by-step solution

A_r= | array ccc r & 1 & n^2 2 + 2 r & 2 & n^2- 3 r-2 & 3 & n(3 n-1) 2 array | 2 ~A ₁₀- A ₈= | array ccc 20 & 1 & n ^2 2 + 40 & 2 & n ^2- 56 & 3 & n (3 n -1) 2 array |- | array ccc 8 & 1 & n ^2 2 + 16 & 2 & n ^2- 22 & 3 & n (3 n -1) 2 array | aligned & | array ccc 12 & 1 & n^2 2 + 24 & 2 & n^2- 34 & 3 & n(3 n-1) 2 array | & | array ccc 0 & 1 & n^2 2 + 0 & 2 & n^2- -2 & 3 & n(3 n-1) 2 array | & -2 ( (n^2- )- (n^2+2 ) ) & -2(- -2 ) 4 +2 aligned

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