The value of the determinant $\left| \begin{array}{ccc} 2 & 8 & 4 \\ -5 & 6 & -10 \\ 1 & 7 & 2 \end{array} \right|$ is

For non-zero $a, b, c$,if $\Delta = \begin{vmatrix} 1 + a & 1 & 1 \\ 1 & 1 + b & 1 \\ 1 & 1 & 1 + c \end{vmatrix} = 0$,then the value of $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = $

Let $D_1 = \begin{vmatrix} a & b & a+b \\ c & d & c+d \\ a & b & a-b \end{vmatrix}$ and $D_2 = \begin{vmatrix} a & c & a+c \\ b & d & b+d \\ a & c & a+b+c \end{vmatrix}$. Then the value of $\frac{D_1}{D_2}$,where $b \neq 0$ and $ad \neq bc$,is:

Verify Property $1$ for $\Delta=\left|\begin{array}{ccc}2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7\end{array}\right|$

If $a=1+2+4+\cdots$ up to $n$ terms,$b=1+3+9+\cdots$ up to $n$ terms and $c=1+5+25+\cdots$ up to $n$ terms,then $\Delta=\left|\begin{array}{ccc}a & 2b & 4c \\ 2 & 2 & 2 \\ 2^n & 3^n & 5^n\end{array}\right|=$

If $\Delta = \begin{vmatrix} x & y & z \\ p & q & r \\ a & b & c \end{vmatrix}$,then $\begin{vmatrix} x & 2y & z \\ 2p & 4q & 2r \\ a & 2b & c \end{vmatrix}$ equals