GATE EC 2014 Question Paper (16-Feb-2014) (Shift 1)

In a PCM system, the signal m(t) = {sin (100 πt) + cos (100 πt)} V is sampled at the Nyquist rate. The samples are processed by a uniform quantizer with step size 0.75 V. The minimum data rate of the PCM system in bits per second is _____.

A binary random variable X takes the value of 1 with probability 1/3. X is input to a cascade of 2 independent identical binary symmetric channels (BSCs) each with crossover probability 1/2. The output of BSCs is the random variables Y₁ and Y₂ as shown in the figure.



The value of H (Y₁) + H (Y₂) in bits is ______.

Given the vector A = (cos x)(sin y)âₓ + (sin x)(cos y) â${}_y$, â${}_y$ denote unit vectors along x,y directions, respectively. The magnitude of the curl of 𝑨 is ______.

A region shown below contains a perfect conducting half-space and air. The surface current $\overrightarrow{K_S}$ on the surface of the perfect conductor is $\overrightarrow{K_S}=\hat{x}2$ amperes per meter. The tangential ${\vec{H}}_t$ field in the air just above the perfect conductor is

Assume that a plane wave in air with an electric field $\vec{E}=10\cos \left(\omega t-3x-\sqrt{3}z\right){\hat{a}}_y$ V/m is incident on a non-magnetic dielectric slab of relative permittivity 3 which covers the region z > 0. The angle of transmission in the dielectric slab is ______ degrees.