If $$L$$ denotes the laplace transform of a function, $$L\left\{ {\sin \,\,at} \right\}$$ will be equal to

A box contains $$10$$ screws, $$3$$ of which are defective. Two screws are drawn at random with replacement. The probability that none of the two screws is defective will be

The vector field $$\,F = x\widehat i - y\widehat j\,\,$$ (where $$\widehat i$$ and $$\widehat j$$ are unit vectors) is

A concrete column carries an axial load of $$450$$ $$kN$$ and a bending moment of $$60$$ $$kN$$-$$m$$ at its base. An isolated footing of size $$2m \times 3m$$ side along the plane of the bending moment is provided under the column. Centers of gravity of column and footing coincide. The net maximum and the minimum pressures in $$kN/{m^2}$$ on soil under the footing are respectively.