The expression $$\mathop {Lim}\limits_{a \to 0} \,{{{x^a} - 1} \over a}\,\,$$ is equal to

The rank of the matrix $$\left[ {\matrix{ 6 & 0 & 4 & 4 \cr { - 2} & {14} & 8 & {18} \cr {14} & { - 14} & 0 & { - 10} \cr } } \right]$$ is

The determinant of matrix $$\left[ {\matrix{ 0 & 1 & 2 & 3 \cr 1 & 0 & 3 & 0 \cr 2 & 3 & 0 & 1 \cr 3 & 0 & 1 & 2 \cr } } \right]$$ is

The survey carried out to delineate natural features, such as hills, rivers, forests and manmade features, such as towns, villages, buildings, roads, transmission lines and canals is classified as