List of top Mathematics Questions on Determinants asked in CBSE CLASS XII

If \( \left| \begin{matrix} 2x & 5 \\ 12 & x \end{matrix} \right| = \left| \begin{matrix} 6 & -5 \\ 4 & 3 \end{matrix} \right| \), then the value of x is:
If $\left| \begin{array}{ccc} -1 & 2 & 4 \\ 1 & x & 1 \\ 0 & 3 & 3x \end{array} \right| = -57$, the product of the possible values of $x$ is:
If \[ A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & -2 \end{bmatrix}, \] then \( |A| \) is:
If \[ A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & -2 \end{bmatrix}, \] then \( |A| \) is:
If $$ \int_{0}^{a} \frac{1}{4 + x^2} \, dx = \frac{\pi}{6}, $$ then the value of \( a \) is: 
If \( a_{ij} \) and \( A_{ij} \) represent the \((i,j)^\text{th}\) element and its cofactor of the matrix: \[ \begin{bmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{bmatrix}, \] respectively, then the value of \( a_{11}A_{21} + a_{12}A_{22} + a_{13}A_{23} \) is: