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NDA2024MathematicsDeterminantsActual

For what value of n is determinant | array ccc C (9,4) & C (9,3) & C (10, n-2) C (11,6) & C (11,5) & C (12, n) C (m, 7) & C (m, 6) & C (m+1, n+1) array |=0 for every m n ?

Options

  1. A4
  2. B5
  3. C6
  4. D7

Correct answer

C. 6

Step-by-step solution

| array ccc C (9,4) & C (9,3) & C (10, n-2) C (11,6) & C (11,5) & C (12, n) C (m, 7) & C (m, 6) & C (m+1,7)- C (m+1, n+1) array |=0 aligned & Applying C ₃ C ₁+ C ₂- C ₃ & | array lcc C (9,4) & C (9,3) & C (10,4)- C (10, n-2) C (11,6) & C (11,5) & C (12,6)- C (12, n) C (m, 7) & C (m, 6) & C (m+1,7)- C (m+1, n+1) array |=0 & Value of determinant =0 & C ₃=0 n-2=4 n=6 . aligned

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