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

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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