If $\begin{vmatrix} 2 & 4 \\ 5 & 1 \end{vmatrix} = \begin{vmatrix} 2x & 4 \\ 6 & x \end{vmatrix}$, then x is equal to :

If $\begin{vmatrix} -a^2 & ab & ac \\ ba & -b^2 & bc \\ ac & bc & -c^2 \end{vmatrix} = 4x$, then $x =$

If $A = \begin{bmatrix} n & 0 & 0 \\ 0 & n & 0 \\ 0 & 0 & n \end{bmatrix}$ and $B = \begin{bmatrix} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{bmatrix}$, then AB is equals to :

If a matrix A is both symmetric and skew symmetric then :

The minimum value of $ax + by$, where $xy = c^2$ and a, b, c are positive, is :

If $57 \equiv x (\bmod 5)$, then the least positive value of $x$ is:

A die is thrown. If A is the event 'the number appearing is a multiple of 3 and B is the event 'the number appearing is even', then A and B are