CUET Mathematics 2026 29th May Shift 1 PYQs

The set of values of K for which the system of equations $\begin{bmatrix} 2 & 3 & 1 \\ 4 & 5 & 0 \\ 1 & K & 3 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 5 \\ 6 \\ 7 \end{bmatrix}$ gives a unique solution is :

Choose the correct statement

A. If any two rows or any two columns are identical or proportional, then value of determinant is Zero.

B. Minor of an element $a_{ij}$ of the determinant of matrix A is the determinant obtained by deleting $i^{th}$ row and $j^{th}$ column

C. If $A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix}$, then A is Skew-symmetric matrix

D. If $A = \begin{bmatrix} 1 & 2 \\ 4 & 5 \end{bmatrix}$, then $(A + A')$ is Symmetric matrix

E. If $|A| = 0$, then A is non-singular matrix

If $\begin{vmatrix} m! & (m+1)! & (m+2)! \\ (m+1)! & (m+2)! & (m+3)! \\ (m+2)! & (m+3)! & (m+4)! \end{vmatrix} = 2k$, where $m$ is a positive integer then which of the following are factors of $k$?

A. $m!$

B. $(m+1)!$

C. $(m+2)!$

D. $(m+3)!$

Choose the correct answer from the options given below: