If $\begin{bmatrix} 2x & -7 \\ 5y & 8 \end{bmatrix} = \begin{bmatrix} 6 & -7 \\ -5 & 3x + y \end{bmatrix}$, then value of $5x - 3y$ is :

If $A=\begin{bmatrix}0 & 1\\0 & 0\end{bmatrix}$, then $A^{1999}$ is equal to

The sum of the minor and the cofactor of the element 6 in the determinant $\begin{vmatrix} 2 & 3 & 1 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{vmatrix}$ is :

$5^{100} (\mod 9) =$

If a square matrix B satisfies $B^2 = I - B$ and $B^n = 5I - 8B$, then the value of n is :

The longest side of a triangle is 4 times the shortest side and the third side is 3 cm shorter than the longest side. If the perimeter of the triangle is at least 69 cm, then the minimum length of the shortest side is:

The area of the triangle with vertices $(1,4), (2,7)$ and $(4,13)$ is :