GATE EC 2021 Question Paper (07-Feb-2021) (Shift 2)

If (1235)ₓ = (3033)${}_y$, where x and y indicate the bases of the corresponding numbers, then

Addressing of a 32K × 16 memory is realized using a single decoder. The minimum number of AND gates required for the decoder is

The block diagram of a feedback control system is shown in the figure.



The transfer function $\frac{Y(s)}{X(s)}$ of the system is

The complete Nyquist plot of the open-loop transfer function G(s) H(s) of a feedback control system is shown in the figure.



If G(s) H(s) has one zero in the right-half of the s-plane. the number of poles that the closed-loop system will have in the right-half of the s-plane is

Consider a rectangular coordinate system (x, y, z) with unit vectors aₓ, a${}_y$, and a${}_z$. A plane wave traveling in the region z ≥ 0 with electric field vector E = 10 cos (2 × 10⁸ t + βz) a${}_y$ is incident normally on the plane at z = 0, where β is the phase constant. The region z ≥ 0 is in free space and the region z < 0 is filled with a lossless medium (permittivity ε = ε₀, permeability μ = 4μ₀, where ε₀ = 8.85 × 10⁻¹² F/m and μ₀ = 4π × 10⁻⁷ H/m). The value of the reflection coefficient is