There are two containers with one containing $$4$$ red and $$3$$ green balls and the other containing $$3$$ blue balls and $$4$$ green balls. One ball is drawn at random from each container. The probability that one of the balls is red and the other is blue will be ___________.

The solution of the differential equation $${{dy} \over {dx}} + {y \over x} = x$$ with the condition that $$y=1$$ at $$x=1$$ is

The square root of a number $$N$$ is to be obtained by applying the Newton $$-$$ Raphson iteration to the equation $$\,{x^2} - N = 0.\,\,$$ If $$i$$ denotes the iteration index, the correct iterative scheme will be

Given two continuous time signals $$x\left( t \right) = {e^{ - t}}$$ and $$y\left( t \right) = {e^{ - 2t}}$$ which exists for $$t>0$$ then the convolution $$z\left( t \right) = x\left( t \right) * y\left( t \right)$$ is ____________.