GATE EE 2015 Set 2 | Continuous Time Signal Laplace Transform Question 2 | Signals and Systems

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 2002

MCQ (Single Correct Answer)

-0.3

Let Y(s) be the Laplace transformation of the function y(t), then the final value of the function is

$$\underset{s\rightarrow0}{L\mathrm{im}\;}Y\left(s\right)$$

$$\underset{s\rightarrow\infty}{L\mathrm{im}\;}Y\left(s\right)$$

$$\underset{s\rightarrow0}{L\mathrm{im}\;}sY\left(s\right)$$

$$\underset{s\rightarrow\infty}{L\mathrm{im}\;}sY\left(s\right)$$

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Electric Circuits

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

Electromagnetic Fields

Time Varying Fields Electrostatics Magnetostatics

Signals and Systems

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

Electrical Machines

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Engineering Mathematics

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

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

Power Electronics

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