A 3 phase, 50 Hz, 6 pole induction motor has a rotor resistance of 0.1 Ω and reactance of 0.92 Ω. Neglect the voltage drop in stator and assume that the rotor resistance is constant. Given that the full load slip is 3%, the ratio of maximum torque to full load torque is

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