GATE EC 2020 Question Paper (02-Feb-2020) (Shift 2)

The components in the circuit given below are ideal. If R = 2 kΩ and C = 1 μF, the -3 dB cut-off frequency of the circuit in Hz is

For the modulated signal x(t) = m(t) cos (2πf${}_c$ t), the message signal m(t) = 4 cos (1000πt) and the carrier frequency f${}_c$ is 1 MHz. The signal x(t) is passed through a demodulator, as shown in the figure below. The output y(t) of the demodulator is

For an infinitesimally small dipole in free space, the electric field E${}_{\theta }$ in the far-field is proportional to (e${}^{-jkr}$ /r)sin θ, where k = 2π/λ. A vertical infinitesimally small electric dipole (δl ≪ λ) is placed at a distance h (h > 0) above an infinite ideal conducting plane, as shown in the figure. The minimum value of h, for which one of the maxima in the far-field radiation pattern occurs at θ = 60°, is

In the voltage regulator shown below, V₁ is the unregulated input at 15 V. Assume V${}_{BE}$ = 0.7 V and the base current in negligible for both the BJTs. If the regulated output V₀ is 9 V, the value of R₂ is _______ Ω

The magnetic field of a uniform plane wave in vacuum is given by:

$\vec{H}\left(x,y,z,t\right)=\left({\hat{a}}_x+2{\hat{a}}_y+b{\hat{a}}_z\right)\cos \left(\omega t+3x-y-z\right)$

The value of b is