CUET Mathematics 2025 16 May Shift 1 PYQs

If $A, B$ and $C$ are three singular matrices given by $A=\left[\begin{array}{ll}1 & 4 \\ 3 & 2 a\end{array}\right], B=\left[\begin{array}{ll}3 b & 5 \\ a & 2\end{array}\right]$ and $C=\left[\begin{array}{cc}a+b+c & c+1 \\ a+c & c\end{array}\right]$, then the value of $a b c$ is :

If $\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix}$, where a, b and c are non zero constants, then the value of $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$ is

If $\begin{bmatrix} x-y & 0 \\ x+y & 1 \end{bmatrix}$ is an identity matrix and $\begin{bmatrix} x & y \\ z & x \end{bmatrix}$ is a singular matrix then: