If $a \ne p,b \ne q,c \ne r$ and $\left| {\,\begin{array}{*{20}{c}}p&b&c\\{p + a}&{q + b}&{2c}\\a&b&r\end{array}\,} \right|$ =$ 0$, then $\frac{p}{{p – a}} + \frac{q}{{q – b}} + \frac{r}{{r – c}} = $

Evaluate the determinants

$\left|\begin{array}{ccc}
3 & -4 & 5 \\
1 & 1 & -2 \\
2 & 3 & 1
\end{array}\right|$

The cubic $\left| {\begin{array}{*{20}{c}}
  0&{a – x}&{b – x} \\ 
  { – a – x}&0&{c – x} \\ 
  { – b – x}&{ – c – x}&0 
\end{array}} \right| = 0$ has a reperated root in $x$ then,

If the system of equations $2x + 3y – z = 0$, $x + ky – 2z = 0$ and  $2x – y + z = 0$ has a non -trivial solution $(x, y, z)$, then $\frac{x}{y} + \frac{y}{z} + \frac{z}{x} + k$ is equal to