GATE EC 2017 Question Paper (05-Feb-2017) (Shift 2)

A modulating signal given by x(t) = 5 sin (4π 10³t - 10π cos 2π 10³t) V is fed to a phase modulator with phase deviation constant kₚ = 5 rad/V. If the carrier frequency is 20 kHz, the instantaneous frequency (in kHz) at t = 0.5 ms is ___________.

Consider a binary memoryless channel characterized by the transition probability diagram shown in the figure.



The channel is

An electron (q₁) is moving in free space with velocity 10⁵ m/s towards a stationary electron (q₂) far away. The closest distance that this moving electron gets to the stationary electron before the repulsive force diverts its path is _________ × 10⁻⁸ m.

[Given, mass of electron m = 9.11 × 10⁻³¹ kg, charge of electron e = -1.6 × 10⁻¹⁹ C, and permittivity ε₀ = (1/36π) × 10⁻⁹ F/m]

Standard air-filled rectangular waveguides of dimensions a = 2.29 cm and b = 1.02 cm are designed for radar applications. It is desired that these waveguides operate only in the dominant TE₁₀ mode with the operating frequency at least 25% above the cutoff frequency of the TE₁₀ mode but not higher than 95% of the next higher cutoff frequency. The range of the allowable operating frequency f is

The permittivity of water at optical frequencies is 1.75 ε₀. It is found that an isotropic light source at a distance d under water forms an illuminated circular area of radius 5 m, as shown in the figure. The critical angle is θ${}_c$.



The value of d (in meter) is _________.