GATE EC question library

Consider the following figure The current in the $1\Omega$ resistor in $\text{Amps}$ is

A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ denote incident, reflected, and transmitted electric field vectors associated with the wave. The angle of incidence $\theta_{i}$ and the expression for $\vec{E_{i}}$ are

A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ denote incident, reflected, and transmitted electric field vectors associated with the wave. The expression for $\vec{E_{r}}$ is

The state diagram of a system is shown below. A system is described by the state-variable equations $$\dot{X}= AX+Bu;\:\: y = CX+Du$$ The state-variable equations of the system shown in the figure above are

The state diagram of a system is shown below. A system is described by the state-variable equations $$\dot{X}= AX+Bu;\:\: y = CX+Du$$ The state transition matrix $e^{At}$ of the system shown in the figure above is