CUET Mathematics 2025 29 May Shift 2 PYQs

Let $AX = B$ be a system of three linear equations in three variables. Then the system has

(A) a unique solutions if $|A| = 0$

(B) a unique solutions if $|A| \neq 0$

(C) no solutions if $|A| = 0$ and (adj A) $B \neq 0$

(D) infinitely many solutions if $|A| = 0$ and (adj A)$B = 0$

Choose the correct answer from the options given below:

If $C_{ij}$ represents the cofactor of element $a_{ij}$ of the matrix $A = \begin{bmatrix} 2 & -1 & 3 \\ 1 & 2 & 0 \\ 4 & 1 & 5 \end{bmatrix}$ then the value of $C_{23} + C_{21} - C_{22}$ is

Let $A = \begin{bmatrix} 0 & 2\alpha+1 \\ \ 1& \beta \end{bmatrix}$ and $B = \begin{bmatrix} b_1 \ b_2 \end{bmatrix}$ be a skew symmetric matrix of order 2 such that $b_{12} = 1$. If $AB = I_2$ where $I_2$ is identity matrix of order 2, then