JEE Main 2022 · 30 Jul · Shift 2 · Mathematics Q64

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MathematicsSingle correct+4 / -1Question 64 of 90

Let A be a matrix and $\begin{bmatrix}1&2\\0&1\end{bmatrix}A\begin{bmatrix}2&0\\-1&1\end{bmatrix}=\begin{bmatrix}1&0\\0&1\end{bmatrix}$ . If |A| and |A $^2$ | are the roots of the quadratic equation $ax^2+bx+3=0$ , then a + b − ab is equal to

−34

−390

438

Answer and worked solution

Official answer: D

Determinant. $1\cdot|A|\cdot2=1$ , so $|A|=\frac12$ and $|A^2|=\frac14$ .

Quadratic. Product $\frac18=\frac3a$ gives $a=24$ ; sum $\frac34=-\frac ba$ gives $b=-18$ . $a+b-ab=6+432=438$ .

(D)

Topics:Determinants and properties Roots and coefficients

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JEE Main 2022 · 30 Jul · Shift 2, Mathematics question 64