GATE EE 2024 | Continuous Time Signal Laplace Transform Question 1 | Signals and Systems

GATE EE 2024

MCQ (Single Correct Answer)

-0.33

If $u(t)$ is the unit step function, then the region of convergence (ROC) of the Laplace transform of the signal $x(t) = e^{t^2}[u(t-1)-u(t-10)]$ is

$-\infty < \text{Re}(s) < \infty$

$\text{Re}(s) \ge 10$

$\text{Re}(s) \le 1$

$1 \le \text{Re}(s) \le 10$

GATE EE 2015 Set 2

MCQ (Single Correct Answer)

-0.3

The Laplace transform of f(t)=$$2\sqrt{t/\mathrm\pi}$$ is $$s^{-3/2}$$. The Laplace transform of g(t)=$$\sqrt{1/\mathrm{πt}}$$ is

$$\left(3s^{-5/2}\right)/2$$

$$s^{-1/2}$$

$$s^{1/2}$$

$$s^{3/2}$$

GATE EE 2013

MCQ (Single Correct Answer)

-0.3

Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?

All the poles of the system must lie on the left side of the j$$\mathrm\omega$$ axis

Zeros of the system can lie anywhere in the s-plane

All the poles must lie within $$\left|s\right|=1$$

All the roots of the characteristic equation must be located on the left side of the j$$\mathrm\omega$$ axis

GATE EE 2012

MCQ (Single Correct Answer)

-0.3

The unilateral Laplace transform of f(t) is $$\frac1{s^2\;+\;s\;+\;1}$$. The unilateral Laplace transform of tf(t) is

$$-\frac s{\displaystyle\left(s^2\;+\;s\;+\;1\right)^2}$$

$$-\frac{2s+1}{\displaystyle\left(s^2\;+\;s\;+\;1\right)^2}$$

$$\frac s{\displaystyle\left(s^2\;+\;s\;+\;1\right)^2}$$

$$\frac{2s+1}{\displaystyle\left(s^2\;+\;s\;+\;1\right)^2}$$

GATE EE Subjects

Browse all chapters by subject

Electric Circuits

Network Elements Transient Response Two Port Networks Sinusoidal Steady State Analysis Network Theorems Three Phase Circuits Graph Theory

Electrical Machines

Induction Machines D.C Machines Transformers Synchronous Machines

Engineering Mathematics

Linear Algebra Differential Equations Probability and Statistics Complex Variable Transform Theory Numerical Methods Calculus Vector Calculus

Signals and Systems

Continuous Time Periodic Signal Fourier Series Sampling Theorem Miscellaneous Continuous Time Signal Fourier Transform Linear Time Invariant Systems Continuous and Discrete Time Signals Discrete Time Signal Z Transformation Continuous Time Signal Laplace Transform

Power Electronics

Power Semiconductor Devices Ac Voltage Controllers Single and Three Phase Rectifier Choppers and Commutation Techniques Inverters

Power System Analysis

Power System Stability Load Flow Studies Parameters and Performance of Transmission Lines High Voltage Dc Transmission Circuit Breaker Symmetrical Components and Symmetrical and Unsymmetrical Faults Per Unit System Power Generation Cost Switch Gear and Protection Generating Power Station

Digital Electronics

Boolean Algebra Combinational Circuits Logic Gates Logic Families and Memories Minimization Sequential Circuits Analog to Digital and Digital to Analog Converter Microprocessor

Analog Electronics

Operational Amplifier 555 Timer Small Signal Modeling Bjt and Mosfet Biasing Diode Circuits and Applications Feedback Amplifiers and Oscillator Circuits Frequency Response

Electromagnetic Fields

Time Varying Fields Electrostatics Magnetostatics

Control Systems

Time Response Analysis State Variable Analysis Basics of Control System Root Locus Techniques Block Diagram and Signal Flow Graph Controller and Compensator Polar Nyquist and Bode Plot Routh Hurwitz Stability

Electrical and Electronics Measurement

Basic of Indicating Instruments Error Analysis and Measurement Cathode Ray Oscilloscope Measurement of Resistance and A.C Bridges Digital Voltmeters Questions Potentiometer and Instrument Transformers Measurement of Energy and Power

General Aptitude

Verbal Ability Logical Reasoning Numerical Ability