Find the area of the triangle whose vertices are $(3,8),(-4,2)$ and $(5,1)$

Number of triplets of $a, b \, \& \,c$ for which the system of equations,$ax – by = 2a – b$ and $(c + 1) x + cy = 10 – a + 3 b$ has infinitely many solutions and $x = 1, y = 3$ is one of the solutions, is :

The number of integers $x$ satisfying $-3 x^4+\operatorname{det}\left[\begin{array}{ccc}1 & x & x^2 \\ 1 & x^2 & x^4 \\ 1 & x^3 & x^6\end{array}\right]=0$ is equal to

The value of the determinant $\left| {\,\begin{array}{*{20}{c}}1&2&3\\3&5&7\\8&{14}&{20}\end{array}\,} \right|$is

The ordered pair $(a, b)$, for which the system of linear equations  $3 x-2 y+z=b$  ;  $5 x-8 y+9 z=3$  ;  $2 x+y+a z=-1$ has no solution, is