GATE EC 2016 Question Paper (31-Jan-2016) (Shift 1)

A discrete memoryless source has an alphabet {a₁, a2, a3, a4} with corresponding probabilities $\left\{\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{8}\right\}$. The minimum required average codeword length in bits to represent this source for error-free reconstruction is ________

A speech signal is sampled at 8 kHz and encoded into PCM format using 8 bits/sample. The PCM data is transmitted through a baseband channel via 4-level PAM. The minimum bandwidth (in kHz) required for transmission is ________

A uniform and constant magnetic field B ẑ. B̅ exists in the ̂ z direction in vacuum. A particle of mass m with a small charge q is introduced into this region with an initial velocity v = x̂vₓ + ẑv${}_z$. Given that B, m, q, vₓ, and v${}_z$ are all non-zero, which one of the following describes the eventual trajectory of the particle?

Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium be expressed as $\vec{\mathrm{E}}=\hat{\mathrm{x}}{\mathrm{E}}_{\mathrm{x}}{\mathrm{e}}^{-(\omega \mathrm{t}-\beta \mathrm{z})}$ , where the propagation constant $\beta$ is a function of the angular frequency $\omega$. Assume that $\beta (\omega )$ and ${\mathrm{E}}_{\mathrm{x}}$ are known and are real. From the information available, which one of the following CANNOT be determined?

Light from free space is incident at an angle θ₁to the normal of the facet of a step-index large core optical fibre. The core and cladding refractive indices are n₁ = 1.5 and n₂ = 1.4, respectively.



The maximum value of θ₁(in degrees) for which the incident light will be guided in the core of the fibre is ________.