NCERT Exemplar MCQ Quiz

If \(\mathrm{A}=\left[\begin{array}{ccc}2 & \lambda & -3 \\ 0 & 2 & 5 \\ 1 & 1 & 3\end{array}\right]\), then \(\mathrm{A}^{-1}\) exists if

Let \(\Delta=\left|\begin{array}{ccc}\mathrm{A} x & x^2 & 1 \\ \mathrm{~B} y & y^2 & 1 \\ \mathrm{C} z & z^2 & 1\end{array}\right|\) and \(\Delta_1=\left|\begin{array}{ccc}\mathrm{A} & \mathrm{B} & \mathrm{C} \\ x & y & z \\ z y & z x & x y\end{array}\right|\), then

If \(\left|\begin{array}{cc}2 x & 5 \\ 8 & x\end{array}\right|=\left|\begin{array}{cc}6 & -2 \\ 7 & 3\end{array}\right|\), then value of \(x\) is

If A, B and C are angles of a triangle, then the determinant \(\left|\begin{array}{ccc}-1 & \cos \mathrm{C} & \cos \mathrm{B} \\ \cos \mathrm{C} & -1 & \cos \mathrm{~A} \\ \cos \mathrm{~B} & \cos \mathrm{~A} & -1\end{array}\right|\) is equal to

If \(x, y, z\) are all different from zero and \(\left|\begin{array}{ccc}1+x & 1 & 1 \\ 1 & 1+y & 1 \\ 1 & 1 & 1+z\end{array}\right|=0\), then value of \(x^{-1}+y^{-1}+z^{-1}\) is

If A and B are invertible matrices, then which of the following is not correct?