The following four vector fields are given in cartesian coordinate system. The vector field which does not satisfy the property of magnetic flux density 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

Given a system of equations $$$x + 2y + 2z = {b_1}$$$ $$$5x + y + 3z = {b_2}$$$
Which of the following is true its solutions