JEE Main 2015 · 11 Apr · Shift 1 · Mathematics Q65

MathematicsSingle correct+4 / -1Question 65 of 90

If
$\begin{vmatrix}x^2+x&x+1&x-2\\2x^2+3x-1&3x&3x-3\\x^2+2x+3&2x-1&2x-1\end{vmatrix}=ax-12,$
then 'a' is equal to :

−12

−24

Answer and worked solution

Official answer: B

The determinant is linear in $x$ .

At $x=0$ it is $-12$ , matching the constant term.
At $x=1$ the rows are $(2,2,-1)$ , $(4,3,0)$ and $(6,1,1)$ , giving $6-8+14=12$ .

So $a-12=12$ and $a=24$ .

JEE Main 2015 · 11 Apr · Shift 1, Mathematics question 65