The value of the integral $$\int\limits_{ - a}^a {{{dx} \over {1 + {x^2}}}} $$

A box contains $$2$$ washers, $$3$$ nuts and $$4$$ bolts. Items are drawn from the box at random one at a time without replacement. The probability of drawing $$2$$ washers first followed by $$3$$ nuts and subsequently the $$4$$ bolts is

The blasius equation $$\,{{{d^3}f} \over {d{\eta ^3}}} + {f \over 2}\,{{{d^2}f} \over {d{\eta ^2}}} = 0\,\,\,\,$$ is a

The Laplace transform of $$f\left( t \right)$$ is $${1 \over {{s^2}\left( {s + 1} \right)}}.$$
The function