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

Electromagnetic Fields

Time Varying Fields Electrostatics Magnetostatics

Signals and Systems

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

Engineering Mathematics

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

General Aptitude

Verbal Ability Logical Reasoning Numerical Ability

Power Electronics

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

Power System Analysis

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

Analog Electronics

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

Control Systems

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

Digital Electronics

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

Electrical Machines

Induction Machines D.C Machines Synchronous Machines Transformers

Electric Circuits

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

Electrical and Electronics Measurement

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