IIT JEE 1982 Maths - 'Adapted' - Subjective to Multi-Correct Q11

Algebra Level pending

Let

\( \begin{vmatrix} x^2+x & x+1 & x-2\\ 2x^2+3x-1 & 3x & 3x-3\\ x^2+2x+3 & 2x-1 & 2x-1\\ \end{vmatrix} = xA+B\)

where A and B are determinants independent of x and of order 3. Then which of the following is/are incorrect?

  • (A) \(det(A)=-12\)
  • (B) \(det(B)=24\)
  • (C) \(det(A)•det(B)=-288\)
  • (D) \(det(A)+det(B)=12\)

Enter your answer as a 4-digit string of 1s and 9s \(-\) 1 for correct option, 9 for wrong. For example: if \(A\) and \(B\) are correct, and \(C\) and \(D\) are incorrect, enter 1199. None, one or all may also be correct.


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