If the determinant of the matrix $$\left[ {\matrix{ 1 & 3 & 2 \cr 0 & 5 & { - 6} \cr 2 & 7 & 8 \cr } } \right]$$ is $$26,$$ then the determinant of
the matrix $$\left[ {\matrix{ 2 & 7 & 8 \cr 0 & 5 & { - 6} \cr 1 & 3 & 2 \cr } } \right]$$ is

If $$y = \left| x \right|$$ for $$x < 0$$ and $$y=x$$ for $$x \ge 0$$ then

If $$\varphi \left( x \right) = \int\limits_0^{{x^2}} {\sqrt t \,dt\,} $$ then $${{d\varphi } \over {dx}} = \_\_\_\_\_\_\_.$$

For the differential equation $$f\left( {x,y} \right){{dy} \over {dx}} + g\left( {x,y} \right) = 0\,\,$$ to be exact is