GATE Signals and Systems: Laplace and z-transforms – Previous Year Questions

7 GATE previous year questions on Laplace and z-transforms (Signals and Systems, Instrumentation Engineering) with answers and explanations, from every paper.

1. GATE 2021 IN Q16 (1 mark, Multiple choice) – Let u(t) be the unit step. The bilateral Laplace transform of f(t)=etu(-t) is .
2. GATE 2022 IN Q11 (1 mark, Multiple choice) – The input x(t) and output y(t) satisfy dy(t)/dt+y(t)=3x(t-3)u(t-3), where u(t) is the unit-step function. The transfer function is .
3. GATE 2022 IN Q40 (2 marks, Multiple choice) – The signal x(t)=(t-1)2u(t-1), where u is the unit step, has Laplace transform X(s). The value of X(1) is .
4. GATE 2023 IN Q37 (2 marks, Multiple choice) – The Laplace transform of x(t)=e-3tu(t-5), where u is the unit step, is
5. GATE 2024 IN Q38 (2 marks, Multiple choice) – For x[n]=cases(0.2)n,&0 n7\\0,&otherwisecases, the region of convergence of its z-transform consists of
6. GATE 2024 IN Q40 (2 marks, Multiple choice) – A signal has bilateral Laplace transform X(s)=1/(s2+13s+42) with region of convergence -7<Re(s)<-6. If u(t) is the unit step, which signal is x(t)?
7. GATE 2026 IN Q43 (2 marks, Multiple choice) – Given two signals x(t)=u(t-2)-u(t-3) and y(t)=e-4tu(t), if z(t)=x(t)*y(t), then Z(s) is .