GATE EE 2014 Question Paper (02-Mar-2014) (Shift 2)

A perfectly conduction metal plate is placed in x-y plane in a right handed coordinate system. A charge of +32πε₀√2 columbs is placed at coordinate (0, 0, 2). ϵ₀ is the permittivity of free space. Assume $\hat{i},\hat{j},\hat{k}$ to be unit vectors along x, y and z axes respectively. At the coordinate. (√2, √2, 0), the electric field vector $\vec{E}$ (Newtons/Columb) will be

A series RLC circuit is observed at two frequencies. At ω₁ = 1 k rad/s, we note that source voltage V₁ = 100∠0°V results in current I₁ = 0.03∠31° A. At ω₂ = 2 k rad/s, the source voltage V₂ = 100∠0° V results in a current I₂ = 2∠0° V A. The closest values for R, L, C out of the following options are

A continuous-time LTI system with system function H(ω) has the following pole-zero plot. For this system, which of the alternatives is TRUE?

A sinusoid x(t) of unknown frequency is sampled by an impulse train of period 20 ms. The resulting sample train is next applied to an ideal lowpass filter with cutoff at 25 Hz. The filter output is seen to be a sinusoid of frequency 20 Hz. This means that x(t) is

A different non constant even function x(t) has a derivative y(t), and their respective Fourier Transforms are X(ω) and Y(ω). Which of the following statements is TRUE