List of top Mathematics Questions on Properties of Determinants asked in MET

If \(A+B+C=\pi\), then \[ \begin{vmatrix} \sin(A+B+C) & \sin B & \cos C -\sin B & 0 & \tan A \cos(A+B) & -\tan A & 0 \end{vmatrix} \] is equal to

If \( x, y, z \) are all positive and are the \( p \)th, \( q \)th and \( r \)th terms of a geometric progression respectively, then the value of the determinant \( \begin{vmatrix} \log x & p & 1 \\ \log y & q & 1 \\ \log z & r & 1 \end{vmatrix} \) equals

The value of \[ \begin{vmatrix} 1 & a & b + c \\ 1 & b & c + a \\ 1 & c & a + b \end{vmatrix} \] is:

If $A$ is a square matrix of order 3 and $|A| = 5$, then $|adj A|$ is: