GATE EE 2022 Question Paper (05-Feb-2022) (Shift 2)

Let a causal LTI system be governed by the following differential equation

$\mathrm{y}(\mathrm{t})+\frac{1}{4}\frac{\mathrm{dy}}{\mathrm{dt}}=2x(\mathrm{t})$ where x(𝑡) and y(𝑡) are the input and output respectively.

Its impulse response is

Let an input x(t) = 2 sin(10πt) + 5 cos(15πt) + 7 sin(42πt) + 4 cos(45πt) is passed through an LTI system having an impulse response

$\mathrm{h}(\mathrm{t})=2\left(\frac{\sin (10\pi \mathrm{t})}{\pi \mathrm{t}}\right)\cos (40\pi \mathrm{t})$

The output of the system is

Let the probability density function of a random variable x be given as

f(x) = ae${}^{-2|x|}$

The value of ‘a’ is __________.

Consider the system as shown below



where y(t) = x(e${}^t$). The system is

A star-connected 3-phase, 400 V, 50 kVA, 50 Hz synchronous motor has a synchronous reactance of 1 ohm per phase with negligible armature resistance. The shaft load on the motor is 10 kW while the power factor is 0.8 leading. The loss in the motor is 2 kW. The magnitude of the per phase excitation emf of the motor, in volts, is __________. (round off to nearest integer).