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# Multiple choice question for engineering

## Set 1

1. Which of the following transfer function will have the greatest maximum overshoot?
a) 9/(s2+2s+9)
b) 16/(s2+2s+16)
c) 25/(s2+2s+25)
d) 36/(s2+2s+36)

Answer: d [Reason:] Comparing the characteristic equation with the standard equation the value of the damping factor is calculated and the value for the option d is minimum hence the system will have the maximum overshoot .

2. A system generated by The ramp component in the forced response will be:
a) t u(t)
b) 2t u(t)
c) 3t u(t)
d) 4t u(t)

Answer: b [Reason:] Laplace transforming sY(s) + 2Y(s)=4/s2 Taking the inverse Laplace transform the forced term is 2t u(t).

3. The system in originally critically damped if the gain is doubled the system will be :
a) Remains same
b) Overdamped
c) Under damped
d) Undamped

Answer: c [Reason:] hence due to this G lies between 0 and 1.

4. Let c(t) be the unit step response of a system with transfer function K(s+a)/(s+K). If c(0+) = 2 and c(∞) = 10, then the values of a and K are respectively.
a) 2 and 10
b) -2 and 10
c) 10 and 2
d) 2 and -10

Answer: c [Reason:] Applying initial value theorem which state that the initial value of the system is at time t =0 and this is used to find the value of K and final value theorem to find the value of a.

5. The damping ratio and peak overshoot are measures of:
a) Relative stability
b) Speed of response
c) Steady state error
d) Absolute stability

Answer: b [Reason:] Speed of response is the speed at which the response takes the final value and this is determined by damping factor which reduces the oscillations and peak overshoot as the peak is less then the speed of response will be more.

6. Find the type and order of the system given below: a) 2,3
b) 2,2
c) 3,3
d) None of the mentioned

Answer: Type = 2 which is the number of poles at the origin and order is the highest power of the characteristic equation.

7. A system has a complex conjugate root pair of multiplicity two or more in its characteristic equation. The impulse response of the system will be:
a) A sinusoidal oscillation which decays exponentially; the system is therefore stable
b) A sinusoidal oscillation with a time multiplier ; the system is therefore unstable
c) A sinusoidal oscillation which rises exponentially ; the system is therefore unstable
d) A dc term harmonic oscillation the system therefore becomes limiting stable

Answer: c [Reason:] Poles are the roots of the denominator of the transfer function and on imaginary axis makes the system stable but multiple poles makes the system unstable.

8. The forward path transfer function is given by G(s) = 2/s(s+3). Obtain an expression for unit step response of the system.
a) 1+2e-t+e-2t
b) 1+e-t-2e-2t
c) 1-e-t+2e-2t
d) 1-2e-t+e+2t

Answer: d [Reason:] C(s)/R(s) = s/(s2+3s+2) C(s) = 1/s-2/s+1+1/s+2 c(t) = 1-2e-t+e+2t.

9. Find the initial and final values of the following function:
F(s) = 12(s+1)/s(s+2)^2(s+3)
a) 1,∞
b) 0,∞
c) ∞,1
d) 0,1

Answer: d [Reason:] Using final and initial values theorem directly to find initial and final values but keeping in mind that final value theorem is applicable for stable systems only.

10. The step response of the system is c(t) = 10+8e-t-4/8e-2t . The gain in time constant form of transfer function will be:
a) -7
b) 7
c) 7.5
d) -7.5

Answer: d [Reason:] Differentiating the equation and getting the impulse response and then taking the inverse Laplace transform and converting the form into time constant form we get K = -7.5.

## Set 2

1. Which of the following transfer function will have the greatest maximum overshoot?
a) 9/(s2+2s+9)
b) 16/(s2+2s+16)
c) 25/(s2+2s+25)
d) 36/(s2+2s+36)

Answer: d [Reason:] Comparing the characteristic equation with the standard equation the value of the damping factor is calculated and the value for the option d is minimum hence the system will have the maximum overshoot .

2. A system generated by The ramp component in the forced response will be:
a) t u(t)
b) 2t u(t)
c) 3t u(t)
d) 4t u(t)

Answer: b [Reason:] Laplace transforming sY(s) + 2Y(s)=4/s2 Taking the inverse Laplace transform the forced term is 2t u(t).

3. The system in originally critically damped if the gain is doubled the system will be :
a) Remains same
b) Overdamped
c) Under damped
d) Undamped

Answer: c [Reason:] hence due to this G lies between 0 and 1.

4. Let c(t) be the unit step response of a system with transfer function K(s+a)/(s+K). If c(0+) = 2 and c(∞) = 10, then the values of a and K are respectively.
a) 2 and 10
b) -2 and 10
c) 10 and 2
d) 2 and -10

Answer: c [Reason:] Applying initial value theorem which state that the initial value of the system is at time t =0 and this is used to find the value of K and final value theorem to find the value of a.

5. The damping ratio and peak overshoot are measures of:
a) Relative stability
b) Speed of response
c) Steady state error
d) Absolute stability

Answer: b [Reason:] Speed of response is the speed at which the response takes the final value and this is determined by damping factor which reduces the oscillations and peak overshoot as the peak is less then the speed of response will be more.

6. Find the type and order of the system given below: a) 2,3
b) 2,2
c) 3,3
d) None of the mentioned

Answer: Type = 2 which is the number of poles at the origin and order is the highest power of the characteristic equation.

7. A system has a complex conjugate root pair of multiplicity two or more in its characteristic equation. The impulse response of the system will be:
a) A sinusoidal oscillation which decays exponentially; the system is therefore stable
b) A sinusoidal oscillation with a time multiplier ; the system is therefore unstable
c) A sinusoidal oscillation which rises exponentially ; the system is therefore unstable
d) A dc term harmonic oscillation the system therefore becomes limiting stable

Answer: c [Reason:] Poles are the roots of the denominator of the transfer function and on imaginary axis makes the system stable but multiple poles makes the system unstable.

8. The forward path transfer function is given by G(s) = 2/s(s+3). Obtain an expression for unit step response of the system.
a) 1+2e-t+e-2t
b) 1+e-t-2e-2t
c) 1-e-t+2e-2t
d) 1-2e-t+e+2t

Answer: d [Reason:] C(s)/R(s) = s/(s2+3s+2) C(s) = 1/s-2/s+1+1/s+2 c(t) = 1-2e-t+e+2t.

9. Find the initial and final values of the following function:
F(s) = 12(s+1)/s(s+2)^2(s+3)
a) 1,∞
b) 0,∞
c) ∞,1
d) 0,1

Answer: d [Reason:] Using final and initial values theorem directly to find initial and final values but keeping in mind that final value theorem is applicable for stable systems only.

10. The step response of the system is c(t) = 10+8e-t-4/8e-2t . The gain in time constant form of transfer function will be:
a) -7
b) 7
c) 7.5
d) -7.5

Answer: d [Reason:] Differentiating the equation and getting the impulse response and then taking the inverse Laplace transform and converting the form into time constant form we get K = -7.5.

## Set 3

1. Which of the following is not the feature of modern control system?
a) Quick response
b) Accuracy
c) Correct power level
d) No oscillation

Answer: d [Reason:] For a good control system the speed of response and stability must be high and for the slow and sluggish response is not used and undesirable.

2. The output of the feedback control system must be a function of:
a) Reference input
b) Reference output
c) Output and feedback signal
d) Input and feedback signal

Answer: d [Reason:] Feedback control system has the property of reducing the error and that is by differencing the output with the desired output and as the equation of the output of the system is C=GR/1+GH.

3. The principle of homogeneity and superposition are applied to:
a) Linear time invariant systems
b) Nonlinear time invariant systems
c) Linear time variant systems
d) Nonlinear time invariant systems

Answer: c [Reason:] Superposition theorem states that for two signals additivity and homogeneity property must be satisfied and that is applicable for the LTI systems.

4. In continuous data systems:
a) Data may be continuous function of time at all points in the system
b) Data is necessarily a continuous function of time at all points in the system
c) Data is continuous at the inputs and output parts of the system but not necessarily during intermediate processing of the data
d) Only the reference signal is continuous function of time

Answer: b [Reason:] Continuous signals are the signals having values for the continuous time and if impulse response decays to zero as time approaches infinity, the system is stable.

5. A linear system at rest is subject to an input signal r(t)=1-e-t. The response of the system for t>0 is given by c(t)=1-e-2t. The transfer function of the system is:
a) (s+2)/(s+1)
b) (s+1)/(s+2)
c) 2(s+1)/(s+2)
d) (s+1)/2(s+2)

Answer: c [Reason:] c(t)=1-e-2t R(s)=1/s-1/s+1 C(s)=1/s-1/s+2 Tf=2(s+1)/(s+2).

6. In regenerating the feedback, the transfer function is given by
a) C(s)/R(s)=G(s)/1+G(s)H(s)
b) C(s)/R(s)=G(s)H(s)/1-G(s)H(s)
c) C(s)/R(s)=G(s)/1+G(s)H(s)
d) C(s)/R(s)=G(s)/1-G(s)H(s)

Answer: d [Reason:] Regenerating feedback is positive feedback and it increases the infinitely and hence the speed of response of the system reduces.

7. A control system whose step response is -0.5(1+e-2t) is cascaded to another control block whose impulse response is e-t. What is the transfer function of the cascaded combination?
a) 1/(s+2)(s+1)
b) 1/(s+1)s
c) 1/(s+3)
d) 0.5/(s+1)(s+2)

Answer: a Solution: Laplace transform is the transformation that transforms the time domain into frequency domain and of both the cascaded systems are 1/(s+1)(s+2).

8. A transfer function has two zeroes at infinity. Then the relation between the numerator(N) and the denominator degree(M) of the transfer function is:
a) N=M+2
b) N=M-2
c) N=M+1
d) N=M-1

Answer: b [Reason:] Zeroes at infinity implies two poles at origin hence the type of the system is two and degree of denominator is M=N+2.

9. When deriving the transfer function of a linear element
a) Both initial conditions and loading are taken into account
b) Initial conditions are taken into account but the element is assumed to be not loaded
c) Initial conditions are assumed to be zero but loading is taken into account
d) Initial conditions are assumed to be zero and the element is assumed to be not loaded

Answer: c [Reason:] When deriving the transfer function of a linear element only initial conditions are assumed to be zero, loading cannot be assumed to be zero.

10. If the initial conditions for a system are inherently zero, what does it physically mean?
a) The system is at rest but stores energy
b) The system is working but does not store energy
c) The system is at rest or no energy is stored in any of its part
d) The system is working with zero reference input

Answer: c [Reason:] A system with zero initial condition is said to be at rest since there is no stored energy.

## Set 4

1. The input of a controller is
a) Sensed signal
b) Error signal
c) Desired variable value
d) Signal of fixed amplitude not dependent on desired variable value

Answer: b [Reason:] Controller is the block in the control system that control the input and provides the output and this is the first block of the system having the input as the error signal.

2. Phase lag controller:
a) Improvement in transient response
b) Reduction in steady state error
c) Reduction is settling time
d) Increase in damping constant

Answer: b [Reason:] Phase lag controller is the integral controller that creates the phase lag and does not affect the value of the damping factor and that tries to reduce the steady state error.

3. Addition of zero at origin:
a) Improvement in transient response
b) Reduction in steady state error
c) Reduction is settling time
d) Increase in damping constant

Answer: a [Reason:] Stability of the system can be determined by various factors and for a good control system the stability of the system must be more and this can be increased by adding zero to the system and improves the transient response.

4. Derivative output compensation:
a) Improvement in transient response
b) Reduction in steady state error
c) Reduction is settling time
d) Increase in damping constant

Answer: c [Reason:] Derivative controller is the controller that is also like high pass filter and is also phase lead controller and it is used to increase the speed of response of the system by increasing the damping coefficient.

5. Derivative error compensation:
a) Improvement in transient response
b) Reduction in steady state error
c) Reduction is settling time
d) Increase in damping constant

Answer: d [Reason:] Damping constant reduces the gain, as it is inversely proportional to the gain and as increasing the damping gain reduces and hence the speed of response and bandwidth are both increased.

6. Lag compensation leads to:
a) Increases bandwidth
b) Attenuation
c) Increases damping factor
d) Second order

Answer: b [Reason:] Phase compensation can be lead, lag or lead lag compensation and integral compensation is also known as lag compensation and leads to attenuation which has least effect on the speed but the accuracy is increased.

a) Increases bandwidth
b) Attenuation
c) Increases damping factor
d) Second order

Answer: a [Reason:] High pass filter is similar to the phase lead compensation and leads to increase in bandwidth and also increase in speed of response.

8. Lag-lead compensation is a:
a) Increases bandwidth
b) Attenuation
c) Increases damping factor
d) Second order

Answer: d [Reason:] Lag-Lead compensation is a second order control system which has lead and lag compensation both and thus has combined effect of both lead and lag compensation this is obtained by the differential equation.

9. Rate compensation :
a) Increases bandwidth
b) Attenuation
c) Increases damping factor
d) Second order

Answer: c [Reason:] Damping factor is increased for reducing the oscillations and increasing the stability and speed of response which are the essential requirements of the control system and damping factor is increased by the rate compensation.

10. Negative exponential term in the equation of the transfer function causes the transportation lag.
a) True
b) False

Answer: a [Reason:] Transportation lag is the lag that is generally neglected in systems but for the accurate measurements the delay caused to transport the input from one end to the other is called the transportation lag in the system causes instability to the system.

## Set 5

1. The auto-correlation function of a rectangular pulse of duration T is
a) A rectangular pulse of duration T
b) A rectangular pulse of duration 2T
c) A triangular pulse of duration T
d) A triangular pulse of duration 2T

Answer: d [Reason:] The auto-correlation function is the method of correlating the various instants of the signal with itself and that of a rectangular pulse of duration T is a triangular pulse of duration 2T.

2. The FT of a rectangular pulse existing between t = − T 2/ to t = T / 2 is a
a) Sinc squared function
b) Sinc function
c) Sine squared function
d) Sine function

Answer: b [Reason:] By definition the Fourier transform is the transformation of time domain of signal to frequency domain and that of a rectangular pulse is a sinc function.

3. The system characterized by the equation y(t) = ax(t) + b is
a) Linear for any value of b
b) Linear if b > 0
c) Linear if b < 0
d) Non-linear

Answer: d [Reason:] The system is non-linear because x(t) = 0 does not lead to y (t) = 0, which is a violation of the principle of homogeneity.

4. The continuous time system described by 2 y(t) = x (t2) is
a) Causal, linear and time varying
b) Causal, non-linear and time varying
c) Non causal, non-linear and time-invariant
d) Non causal, linear and time-invariant

Answer: d [Reason:] Y (t) depends upon the future value therefore the system is anticipative and hence is not causal. But as it follows the superposition theorem so it is linear.

5. If G( f) represents the Fourier Transform of a signal g (t) which is real and odd symmetric in time, then G (f) is
a) Complex
b) Imaginary
c) Real
d) Real and non-negative

Answer: b [Reason:] For the real and odd symmetric signal in time domain on the Fourier transform the resulting signal is always imaginary.

6. If a periodic function f(t) of period T satisfies f(t) = −f (t + T/2) , then in its Fourier series expansion
a) The constant term will be zero
b) There will be no cosine terms
c) There will be no sine terms
d) There will be no even harmonics

Answer: b [Reason:] The fourier series will contain the cosine terms if the periodic function f (t) of period T satisfies f (t) = -f(t+T/2), and this can be proved by the basic definition of the fourier transform.

7. Given a unit step function u (t), its time-derivative is:
a) A unit impulse
b) Another step function
c) A unit ramp function
d) A sine function

Answer: a [Reason:] Unit step function is one of the test signals and for the basic standard signals they are interrelated as the function of differentiation and integration as unit step function is the integral of impulse function.

8. The order of a linear constant-coefficient differential equation representing a system refers to the number of
a) Active devices
b) Elements including sources
c) Passive devices
d) None of the mentioned

Answer: d [Reason:] The order of the differential equation is the power of the highest order of the differential term and which refers to the number of poles in the transfer function and practically it refers to the number of components that are energy storing elements .

9. Z-transform converts convolution of time-signals to
b) Subtraction
c) Multiplication
d) Division

Answer: c [Reason:] Convolution is the combination of addition and multiplication that is between the same signal or the different signals and convolution in time domain is always multiplication in z domain.

10. Region of convergence of a causal LTI system
a) Is the entire s-plane
b) Is the right-half of s-plane
c) Is the left-half of s-plane
d) Does not exist