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Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE) PDF Download

Q1: If u(t) is the unit step function, then the region of convergence (ROC) of the Laplace transform of the signal Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)is      (2024)
(a) <Re(𝑠)<−∞ < Re(s) < ∞
(b) Re(s) ≥ 10
(c) Re(s) ≤ 1
(d) 1Re(𝑠)101 ≤ Re(s) ≤ 10
Ans:
(a)
Sol: Since x(t) is finite duration signal. So ROC will be −∞ < σ < ∞.

Q2: Which of the following statements is true about the two sided Laplace transform?     (2020)
(a) It exists for every signal that may or may not have a Fourier transform.
(b) It has no poles for any bounded signal that is non-zero only inside a finite time interval.
(c) The number of finite poles and finite zeroes must be equal.
(d) If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace Transform will have no poles.
Ans: 
(b)
Sol: It has no poles for any bounded signal that is nonzero in a finite time interval. This is true as we know for finite amplitude finite width signal ROC is entire s plane and ROC never includes any pole.
It implies for such signals there is no poles. Hence the correct answer is option (B).

Q3: The output response of a system is denoted as y(t), and its Laplace transform is given by Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE) 
The steady state value of y(t) is      (2019)
(a) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)

(b) 10√2
(c) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
(d) 100√2
Ans: (a)
Sol: Steady state value of y(t)
Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Q4: A system transfer function is Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE) and all other coefficients are positive, the transfer function represents a        (2019)
(a) low pass filter
(b) high pass filter
(c) band pass filter
(d) notch filter
Ans
: (a)
Sol: Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)which represents second order low pass filter.

Q5: The inverse Laplace transform of      (2019)
Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)(a) 3te−t + e−t 
(b) 3e−t
(c) 2𝑡𝑒𝑡+𝑒𝑡2te−t + e−t 
(d) 4te−t + e−t 
Ans:
(c)
Sol: Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Q6: Consider a linear time-invariant system with transfer function Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)If the input is cos(t) and the steady state output is Acos(t + α), then the value of A is _________.      (SET-2 (2016))
(a) 0.70
(b) 0.26
(c) 0.96
(d) 1.2
Ans
: (a)
Sol: Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Q7: The transfer function of a system is  Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)The steady state output y(t) is Acos(2t + φ) for the input cos(2t). The values of A and φ, respectively are      (SET-1 (2016))
(a) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)

(b) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
(c) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
(d) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Ans: (b)
Sol: Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Q8: The Laplace Transform of f(t) = e2tsin(5t)u(t) is       (SET-1 (2016))
(a) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)

(b) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
(c) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
(d) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Ans: (a)
Sol: Laplace transform of sin5tu(t) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Q9: The Laplace transform of Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE) The Laplace transform of g(t) = Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE) is       (SET-2 (2015))
(a) 3𝑠5/2/23s−5/2/2
(b) s−1/2
(c) 𝑠1/2s1/2 
(d) 𝑠3/2
Ans:
(b)
Sol: Given that,
Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)By using property of differentiation In time,
Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Q10: Consider an LTI system with transfer function Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)If the input to the system is cos(3t) and the steady state output is Asin(3t + α), then the value of A is       (SET-2 (2014))
(a) 1/30
(b) 1/15
(c) 3/4
(d) 4/3
Ans:
(b)
Sol: Given,
Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)A = 1/15.

Q11: Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?      (2013)
(a) All the poles of the system must lie on the left side of the jω axis
(b) Zeros of the system can lie anywhere in the s-plane
(c) All the poles must lie within |s| = 1
(d) All the roots of the characteristic equation must be located on the left side of the jω axis.
Ans:
(c)
Sol: All poles must lie within |Z| = 1

Q12: Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is      (2013)
Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)(a) u(t)
(b) tu(t)
(c) (t2/2) (u(t))

(d) 𝑒𝑡𝑢(𝑡)e−tu(t)
Ans:
(b)
Sol: Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Q13: Consider the differential equation
Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)The numerical value of Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE) is,      (2012)
(a) -2
(b) -1
(c) 0
(d) 1
Ans:
(d)
Sol: Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Q14: The unilateral Laplace transform of Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE) The unilateral Laplace transform of  tf(t) is       (2012)
(a) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)

(b) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
(c) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
(d) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Ans: (d)
Sol: Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Q15: Let the Laplace transform of a function F(t) which exists for t > 0 be F1(s) and the Laplace transform of its delayed version f(t − τ) be F2(s). Let Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE) be the complex conjugate of F1(s) with the Laplace variable set  s = σ + iω. If  Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE) then the inverse Laplace transform of G(s) is      (2011)
(a) An ideal impulse δ(t)
(b) An ideal delayed impulse δ(t − τ)
(c) An ideal step function u(t)
(d) An ideal delayed step function u (t − τ)
Ans: 
(b)
Sol: Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Q16: Given f(t) and g(t)as shown below:
Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)The Laplace transform of g(t) is       (2010)
(a) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)

(b) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
(c) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
(d) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Ans: (c)
Sol: Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Q17: Given f(t) and g(t)as shown below:
Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)g(t) can be expressed as      (2010)
(a) 𝑔(𝑡)=𝑓(2𝑡3)g(t) = f(2t − 3)
(b) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)

(c) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
(d)  Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Ans: (d)
Sol: Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)Since, g(t) has width of 2-unit and f(t) has 1 unit, therefore we have to first expand f(t) by 2 unit and for this we have to scale f(t) by 1/2.
Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)Now shift it by three unit to get g(t)
Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Q18: The running integration, given by     (2006)
Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)(a) has no finite singularities in its double sided Laplace Transform Y(s)
(b) produces a bounded output for every causal bounded input
(c) produces a bounded output for every anticausal bounded input
(d) has no finite zeroes in its double sided Laplace Transform Y(s)
Ans: 
(d)

Q19: The Laplace transform of a function f(t) is Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE) f(t) approaches      (2005)
(a) 3
(b) 5
(c) 17/2
(d) ∞
Ans:
(a)
Sol:  Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)As F(s) has only left hand poles.
By final value theorem,
Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Q20: Consider the function, Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE) where F(s) is the Laplace transform of the of the function f(t). The initial value of f(t) is equal to      (2004)
(a) 5
(b) 5/2
(c) 5/3
(d) 0
Ans:
(d)
Sol: Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)By initial value theorem,
Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Q21: Let Y(s) be the Laplace transformation of the function y(t), then the final value of the function is       (2002)
(a) lim𝑠0𝑌(𝑠)lims→0 Y(s)
(b) lims→∞ Y(s)
(c) lim𝑠0𝑠𝑌(𝑠)lims→0 sY(s)
(d)  limx→∞ sY(s)  
Ans:
(c)
Sol: Final value = lims→0 sY(s)

Q22: Given the relationship between the input u(t) and the output y(t) to be
Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)the transfer function Y(s)/U(s) is      (2001)
(a) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)

(b) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
(c) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
(d) Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)
Ans: (d)
Sol: Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE)

The document Previous Year Questions- Laplace Transform | Signals and Systems - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Signals and Systems.
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FAQs on Previous Year Questions- Laplace Transform - Signals and Systems - Electrical Engineering (EE)

1. What is the Laplace transform in electrical engineering?
Ans. The Laplace transform is a mathematical technique used in electrical engineering to simplify the analysis of linear time-invariant systems by converting differential equations into algebraic equations.
2. How is the Laplace transform different from the Fourier transform?
Ans. The Laplace transform is used for analyzing systems with exponential signals and is defined for a wider range of functions compared to the Fourier transform, which is mainly used for analyzing systems with sinusoidal signals.
3. Why is the Laplace transform preferred over the Fourier transform in electrical engineering?
Ans. The Laplace transform is preferred over the Fourier transform in electrical engineering because it provides a more comprehensive analysis of systems with exponential signals, including transient and steady-state responses.
4. How do you calculate the Laplace transform of a function in electrical engineering?
Ans. The Laplace transform of a function in electrical engineering is calculated by integrating the function multiplied by an exponential function, e^(-st), where s is a complex frequency variable.
5. What are the applications of the Laplace transform in electrical engineering?
Ans. The Laplace transform is widely used in electrical engineering for analyzing and designing control systems, signal processing, communication systems, and circuit analysis.
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