If the matrix $\begin{bmatrix} a & -2 & 5b \\ 2 & 0 & -15 \\ 15 & 3c & 0 \end{bmatrix}$ is skew-symmetric, then the value of $a^2 + b^2 + c^2$ is:

Matrix $A = \begin{bmatrix} 0 & a & 5 \\ 4 & b & -1 \\ c & 1 & 0 \end{bmatrix}$ is skew - symmetric, then the values of a, b c are :

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

the least non-negative remainder when $3^{17}$ is divided by 7 is :

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

If $A' = \begin{bmatrix} -2 & 3 \\ 1 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} -1 & 0 \\ 2 & 3 \end{bmatrix}$

then $(3A + 2B)'$ is :

If $\begin{bmatrix} 5x + 8 & 7 \\ y + 3 & 10x + 12 \end{bmatrix} = \begin{bmatrix} 2 & 3y + 1 \\ 5 & 0 \end{bmatrix}$, then the value of $5x + 3y$ is equal to :