CUET Mathematics 2026 19th May Shift 2 PYQs

If $XA=(I-A)^2$ where $X, A$ and $I$ are $2\times2$ matrices and $A=\begin{bmatrix}1 & 2\\1 & 4\end{bmatrix}$, then $|X|=$

The set of all values of $\alpha$ for which the system of linear equations

$x + y + z = 1$

$x + 2y + 4z = \alpha$

$x + 4y + 10z = \alpha^2$

is consistent, is

If $A = \begin{bmatrix} 2 & -3 \\ -4 & 7 \end{bmatrix}$ and $2A^{-1} = KI - A$, where K is a real number and I is the identity matrix of order 2, then the value of K is: