GATE IN 2022 Question Paper (06-Feb-2022) (Shift 2)

A signal Vᵢₙ(t) shown is applied from 𝑡 = 0 ms to 𝑡 = 6 ms to the circuit shown. Given the initial voltage across the capacitor is 0.3 V, and that the diode is ideal, the open circuit voltage Vₒᵤₜ(t) at 𝑡 = 5 ms is

The signal flow graph of a system is shown.

The expression for 𝑌(𝑠)/𝑋(𝑠) is _______

Consider the transfer function

${\mathrm{H}}_{\mathrm{c}}(\mathrm{s})=\frac{1}{(\mathrm{s}+1)(\mathrm{s}+3)}$

Bilinear transformation with a sampling period of 0.1 s is employed to obtain the discrete-time transfer function H${}_d$ (z). Then H${}_d$ (z) is _______

A car is moving collinearly with a laser beam emitted by a transceiver. A laser pulse emitted at 𝑡 = 0 s is received back by the transceiver 100 ns (nanoseconds) later after reflection from the car. A second pulse emitted at 𝑡 = 0.1 s is received back 90 ns later. Given the speed of light is 3 × 10⁸ m/s, the average speed of the car in this interval is _____

The signal x(t) = (t - 1)²u(t - 1), where 𝑢(𝑡) is the unit-step function, has the Laplace transform 𝑋(𝑠). The value of 𝑋(1) is____