Find adjoint of each of the matrices : $\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$

Let $\left| {\begin{array}{*{20}{c}}
  {{{\left( {a – x} \right)}^2}}&{{{\left( {a – y} \right)}^2}}&{{{\left( {a – z} \right)}^2}} \\ 
  {{{\left( {b – x} \right)}^2}}&{{{\left( {b – y} \right)}^2}}&{{{\left( {b – z} \right)}^2}} \\ 
  {{{\left( {c – x} \right)}^2}}&{{{\left( {c – y} \right)}^2}}&{{{\left( {c – z} \right)}^2}} 
\end{array}} \right| = \frac{{ – 351}}{8}$ . If $x, y , z$ are the roots of the equation $8t^3 – 62t^2 + 43t -7 = 0$ and satisfy the determinant above, and $a, b, c$ are distinct number then value of $|(a – b) (b – c) (c – a)|$ is

If $\left| {\begin{array}{*{20}{c}}
1&1&1\\
a&b&c\\
{{a^2}}&{{b^2}}&{{c^2}}
\end{array}} \right| = 5$ , then $\left| {\begin{array}{*{20}{c}}
{b{c^2} – {b^2}c}&{{a^2}c – a{c^2}}&{a{b^2} – b{a^2}}\\
{{b^2} – {c^2}}&{{c^2} – {a^2}}&{{a^2} – {b^2}}\\
{c – b}&{a – c}&{b – a}
\end{array}} \right|$ is equal to

If $\Delta=\left|\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right|$ and $\mathrm{A}_{i j}$ is Cofactors of $a_{i j},$ then value of $\Delta$ is given by

Write Minors and Cofactors of the elements of following determinants: $\left|\begin{array}{ccc}1 & 0 & 4 \\ 3 & 5 & -1 \\ 0 & 1 & 2\end{array}\right|$