CUET Mathematics 2026 14th May Shift 2 PYQs

Which of the following systems has only a trivial solution?

The value of the determinant $\Delta=\begin{vmatrix}\cos\alpha\cos\beta & \cos\alpha\sin\beta & -\sin\alpha\\-\sin\beta & \cos\beta & 0\\\sin\alpha\cos\beta & \sin\alpha\sin\beta & \cos\alpha\end{vmatrix}$ is:

If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ m & 2 & n \end{bmatrix}$ is a matrix, such that $AA^T = 9I_3$, then the values of $m$ and $n$ are (where $I_3$ is an identity matrix of order 3)