A fair coin is tossed $$n$$ times. The probability that the difference between the number of heads and tails is $$(n-3)$$ is

The solution for the differential equation $$\,\,{{{d^2}x} \over {d{t^2}}} = - 9x,\,\,$$ with initial conditions $$x(0)=1$$ and $${{{\left. {\,\,\,\,{{dx} \over {dt}}} \right|}_{t = 0}} = 1,\,\,}$$ is

Let $$S$$ be the set of points in the complex plane corresponding to the unit circle. $$\left( {i.e.,\,\,S = \left\{ {z:\left| z \right| = 1} \right\}} \right.$$ Consider the function $$f\left( z \right) = z{z^ * }$$ where $${z^ * }$$ denotes the complex conjugate of $$z.$$ The $$f(z)$$ maps $$S$$ to which one of the following in the complex plane?

Let $$X\left( s \right) = {{3s + 5} \over {{s^2} + 10s + 20}}$$ be the Laplace Transform of a signal $$x(t).$$
Then $$\,x\left( {{0^ + }} \right)$$ is