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# Multiple choice question for engineering

## Set 1

1. Stability of a system implies that :
a) Small changes in the system input does not result in large change in system output
b) Small changes in the system parameters does not result in large change in system output
c) Small changes in the initial conditions does not result in large change in system output
d) All of the above mentioned

### View Answer

Answer: d [Reason:] Stability of the system implies that small changes in the system input, initial conditions, and system parameters does not result in large change in system output.

2. A linear time invariant system is stable if :
a) System in excited by the bounded input, the output is also bounded
b) In the absence of input output tends zero
c) Both a and b
d) System in excited by the bounded input, the output is not bounded

### View Answer

Answer: c [Reason:] A system is stable only if it is BIBO stable and asymptotic stable.

3. Asymptotic stability is concerned with:
a) A system under influence of input
b) A system not under influence of input
c) A system under influence of output
d) A system not under influence of output

### View Answer

Answer: b [Reason:] Asymptotic stability concerns a free system relative to its transient behavior.

4. Bounded input and Bounded output stability notion concerns with :
a) A system under influence of input
b) A system not under influence of input
c) A system under influence of output
d) A system not under influence of output

### View Answer

Answer: a [Reason:] BIBO stability concerns with the system that has input present.

5. If a system is given unbounded input then the system is:
a) Stable
b) Unstable
c) Not defined
d) Linear

### View Answer

Answer: c [Reason:] If the system is given with the unbounded input then nothing can be clarified for the stability of the system.

6. Linear mathematical model applies to :
a) Linear systems
b) Stable systems
c) Unstable systems
d) Non-linear systems

### View Answer

Answer: b [Reason:] As the output exceeds certain magnitude then the linear mathematical model no longer applies.

7. For non-linear systems stability cannot be determined due to:
a) Possible existence of multiple equilibrium states
b) No correspondence between bounded input and bounded output stability and asymptotic stability
c) Output may be bounded for the particular bounded input but may not be bounded for the bounded inputs
d) All of the mentioned

### View Answer

Answer: d [Reason:] For non-linear systems stability cannot be determined as asymptotic stability and BIBO stability concepts cannot be applied, existence of multiple states and unbounded output for many bounded inputs.

8. If the impulse response in absolutely integrable then the system is :
a) Absolutely stable
b) Unstable
c) Linear
d) Stable

### View Answer

Answer: a [Reason:] The impulse response must be absolutely integrable for the system to absolutely stable.

9. The roots of the transfer function do not have any effect on the stability of the system.
a) True
b) False

### View Answer

Answer: b [Reason:] The roots of transfer function also determine the stability of system as they may be real, complex and may have multiplicity of various order.

10. Roots with higher multiplicity on the imaginary axis makes the system :
a) Absolutely stable
b) Unstable
c) Linear
d) Stable

### View Answer

Answer: b [Reason:] Repetitive roots on the imaginary axis makes the system unstable.

11. Roots on the imaginary axis makes the system :
a) Stable
b) Unstable
c) Marginally stable
d) Linear

### View Answer

Answer: c [Reason:] Roots on the imaginary axis makes the system marginally stable.

12. If the roots of the have negative real parts then the response is ____________
a) Stable
b) Unstable
c) Marginally stable
d) Bounded

### View Answer

Answer: d [Reason:] If the roots of the have negative real parts then the response is bounded and eventually decreases to zero.

13. If root of the characteristic equation has positive real part the system is :
a) Stable
b) Unstable
c) Marginally stable
d) Linear

### View Answer

Answer: b [Reason:] The impulse response of the system is infinite when the roots of the characteristic equation has positive real part.

14. A linear system can be classified as :
a) Absolutely stable
b) Conditionally stable
c) Unstable
d) All of the mentioned

### View Answer

Answer: d [Reason:] A system can be stable, unstable and conditionally stable also.

15. ___________ is a quantitative measure of how fast the transients die out in the system.
a) Absolutely stable
b) Conditionally stable
c) Unstable
d) Relative Stability

### View Answer

Answer: d [Reason:] Relative Stability may be measured by relative settling times of each root or pair of roots.

## Set 2

1. The transfer function for the state representation of the continuous time LTI system:
dq(t)/dt=Aq(t)+Bx(t)
Y(t)=Cq(t)+Dx(t)
is given by:
a) C(sI-A)-1B+D
b) B(sI-A)-1B+D
c) C(sI-A)-1B+A
d) D(sI-A)-1B+C

### View Answer

Answer: a [Reason:] Transfer function which is ratio of Laplace output to the Laplace input when the initial conditions are zero and is calculated by using both the equations.

2. System transformation on function H(z) for a discrete time LTI system expressed in state variable form with zero initial condition
a) C(zI-A)-1B+D
b) C(zI-A)-1
c) (zI-A)-1z
d) (zI-A)-1

### View Answer

Answer: a [Reason:] Transfer function which is ratio of Laplace output to the Laplace input when the initial conditions are zero in discrete is same as continuous but in the z-domain.

3. State space analysis is applicable for non-linear systems and for multiple input and output systems.
a) True
b) False

### View Answer

Answer: a [Reason:] State space analysis is the technique that used state variables and state model for the analysis and is applicable for non-linear systems and for multiple input and output systems.

4. Assertion (A): Transfer function approach has limitation that it reveals only the system output for a input and provides no information regarding the internal state of the system.
Reason (R): There may be situations where the output of a system is stable and yet some of the system elements may have a tendency to exceed their specified ratings.
a) Both A and R are true and R is correct explanation of A
b) Both A and R are true but R is not correct explanation of A
c) A is true but R is False
d) A is False but R is True

### View Answer

Answer: a [Reason:] Transfer function approach has limitation over state variable analysis and for that it reveals only the system output for a input and provides no information regarding the internal state of the system.

5. When human being tries to approach an object, his brain acts as,
a) An error measuring device
b) A controller
c) An actuator
d) An amplifier

### View Answer

Answer: b [Reason:] Brain of human being acts as a controller in the human body system as human body is the control system and when human tries to approach an object the brain of the human acts as controller.

6. For two-phase AC servomotor, if the rotor’s resistance and reactance are respectively R and X, its length and diameter are respectively L and D then,
a) X/R and L/D are both small
b) X/R is large but L/D is small
c) X/R is small but L/D is large
d) X/R and L/D are both large

### View Answer

Answer: c [Reason:] Small X/R gives linear speed torque characteristic. Large L/D gives less inertia and good acceleration characteristic.

7. Consider the following statements relating to synchro’s:
1. The rotor of the control transformer is either disc shaped
2. The rotor of the transmitter is so constructed as to have a low magnetic reluctance
3. Transmitter and control transformer pair is used as an error detector
Which of these statements are correct?
a) 1,2 and3
b) 1 and 2
c) 2 and3
d) 1 and 3

### View Answer

Answer: c [Reason:] Rotor of control transformer is rotatory part of the transformer and is made cylindrical in shape so that air gap is practically uniform.

8. Error detector:
a) Armature controlled FHP DC motor
b) A pair of synchronous transmitter and control transformer
c) Tach generator
d) Amplidyne

### View Answer

Answer: a [Reason:] Error detector is the part in the armature controlled FHP DC motor where error detector is the first element that compares the final output with desired output and gives the accurate results.

9. Servomotor:
a) Armature controlled FHP DC motor
b) A pair of synchronous transmitter and control transformer
c) Tach generator
d) Amplidyne

### View Answer

Answer: b [Reason:] Servomotor is a rotary actuator or linear actuator that allows for precise control of angular or linear position, velocity and acceleration a pair of synchronous transmitter and control transformer.

10. Amplifier:
a) Armature controlled FHP DC motor
b) A pair of synchronous transmitter and control transformer
c) Tach generator
d) Amplidyne

### View Answer

Answer: d [Reason:] Amplifier is an amplidyne which is an amplidyne is an electromechanical amplifier invented during World War II by Ernst Alexanderson. It consists of an electric motor driving a DC generator.

## Set 3

1. In liquid level and electrical system analogy, voltage is considered analogous to :
a) Head
b) Liquid flow
c) Liquid flow rate
d) Air flow rate

### View Answer

Answer: a [Reason:] In liquid level and electrical system analogy, voltage is considered analogous to the head which can be pressure head that is the potential energy.

2. The viscous friction co-efficient, in force-voltage analogy, is analogous to:
a) Charge
b) Resistance
c) Reciprocal of inductance
d) Reciprocal of conductance

### View Answer

Answer: b [Reason:] The viscous friction co-efficient in force-voltage analogy, is analogous to resistance of the electrical circuit that can be found out mathematically.

3. In force-voltage analogy, velocity is analogous to:
a) Current
b) Charge
c) Inductance
d) Capacitance

### View Answer

Answer: a [Reason:] In force-voltage analogy, velocity is analogous to the current in force-voltage that is also called series circuit.

4. In thermal-electrical analogy charge is considered analogous to:
a) Heat flow
b) Reciprocal of heat flow
c) Reciprocal of temperature
d) Temperature

### View Answer

Answer: d [Reason:] In thermal-electrical analogy in which heat transfer in the wire or conductor can be related to the temperature.

5. Mass, in force-voltage analogy, is analogous to:
a) Charge
b) Current
c) Inductance
d) Resistance

### View Answer

Answer: c [Reason:] Mass, is analogous to the inductance in the force-voltage analogy in the series form as all the elements of the circuit are connected in the parallel.

6. The transient response of a system is mainly due to:
a) Inertia forces
b) Internal forces
c) Stored energy
d) Friction

### View Answer

Answer: c [Reason:] The transient response of the system is mainly due to stored energy as it is due to the initial conditions which is nothing but the stored energy.

7. ___________ signal will become zero when the feedback signal and reference signs are equal.
a) Input
b) Actuating
c) Feedback
d) Reference

### View Answer

Answer: b [Reason:] Actuating signal is the difference between the feedback signal and the reference signal and when both of the signals are equal then the signal is zero.

8. A signal other than the reference input that tends to affect the value of controlled variable is known as
a) Disturbance
b) Command
c) Control element
d) Reference input

### View Answer

Answer: a [Reason:] Disturbance signal is also the reference signal only there can be multiple inputs in a control system or the other input is called the disturbance signal.

9. The transfer function is applicable to which of the following?
a) Linear and time-in variant systems
b) Linear and time-variant systems
c) Linear systems
d) Non-linear systems

### View Answer

Answer: a [Reason:] The transfer function is different from the state space approach as the transfer function approach is similar to the LTI systems only while the state variable analysis is applicable to the non-linear time variant systems also.

10. From which of the following transfer function can be obtained?
a) Signal flow graph
b) Analogous table
c) Output-input ratio
d) Standard block system

### View Answer

Answer: a [Reason:] The transfer function can be obtained by using signal flow graphs from among these given methods.

## Set 4

1. Electrical time-constant of an armature-controlled dc servomotor is :
a) Equal to mechanical time-constant
b) Smaller than mechanical time-constant
c) Larger than mechanical time-constant
d) Not related to mechanical time-constant

### View Answer

Answer: b [Reason:] Electrical time constant is smaller than the mechanical time constant and hence the delay in the mechanical systems is more than the electrical systems.

2. The open-loop transfer function of a unity feedback system is K/(s^2 (s+5))The system is unstable for
a) K>5
b) K<5
c) K>0
d) All of the mentioned

### View Answer

Answer: d [Reason:] The open loop transfer function of a unity feedback system is used to calculate the conditional stability by using the Routh Hurwitz criteria or the Root locus technique.

3. Peak overshoot of step-input response of an underdamped second-order system is explicitly indicative of
a) Settling time
b) Rise time
c) Natural frequency
d) Damping ratio

### View Answer

Answer: d [Reason:] Peak overshoot refers to the damping of the system as if the damping id less than the peak will be more.

4. A unity feedback system with open-loop transfer function G (s) = 4/[s(s+p)] is critically damped. The value of the parameter p is
a) 4
b) 3
c) 2
d) 1

### View Answer

Answer: a [Reason:] The value of the p can be calculated by comparing the equation with the standard characteristic equation.

5. Polar plot of G (jw) = 1/jw(jw+t) is
a) Crosses the negative real axis
b) Crosses the negative imaginary axis
c) Crosses the positive imaginary axis
d) None of the mentioned

### View Answer

Answer: d [Reason:] Polar plot can be made of the following function by following appropriate steps and thus the plot neither crosses the real axis nor imaginary axis.

6. In optimum time switching curve the system takes :
a) Minimum time in reaching desired location
b) Maximum time in reaching desired location
c) Never reaches
d) No desired location is present

### View Answer

Answer: a [Reason:] If switching is made to occur the crossing of the starting trajectory with the thick line trajectory the system follows the trajectory and reaches the desired output at the minimum time.

7. System with logic switching are :
a) Hang on
b) Bang on
c) Bang-bang
d) Hang out

### View Answer

Answer: c [Reason:] Suitable logic circuitry has to be added to the controller structure for the kind of the switching and such systems are known as the bang-bang control system.

8. Zeroes are defined as:
a) Roots of the denominator of the closed loop transfer function
b) Roots of the numerator of the closed loop transfer function
c) Both of the mentioned
d) None of the mentioned

### View Answer

Answer: b [Reason:] Zeroes are defined as the roots of the numerator of the closed loop system.

9. As zero moves sufficiently left from the origin the effect of zero becomes less pronounced.
a) True
b) False

### View Answer

Answer: a [Reason:] The effect of zero on transient response will be negligible if the zero moves left from the origin due to dominant pole mechanism.

10. Assertion (A): The zeroes on the real axis near the origin are generally avoided in design.
Reason (R): In a sluggish system introduction of zeroes can improve the transient response
a) Both A and R are true and R is correct explanation of A
b) Both A and R are true but R is not correct explanation of A
c) A is true but R is false
d) A is false but R is true

### View Answer

Answer: b [Reason:] The zeroes on the real axis near the origin are generally avoided in design as they cause system instability.

## Set 5

1. With reference to root locus, the complex conjugate roots of the characteristic equation of the O.L.T.F. given below G(s)H(s) =K(s+3)/(s+1)2, lie on
a) Straight line
b) Parabola
c) Circle
d) Semi-circle

### View Answer

Answer: c [Reason:] Complex conjugate roots of the characteristic equation of the O.L.T.F.lie on circle.

2. Determine the centroid of the root locus for the system having G(s)H(s) = K/(s+1)(s2+4s+5)
a) -2.1
b) -1.78
c) -1.66
d) -1.06

### View Answer

Answer: Roots of the open loop transfer function are -1,-2+j, -2-j then centroid =Σreal part of open loop pole-Σreal part of open loop zeroes/P-Z Centroid =(-1-2-2)-0/3 =-5/3 =-1.66.

3. The loop transfer function of an LTI system is G(s)H(s) =K(s+1)(s+5)/s(s+2)(s+3). For K>0, the point on the real axis that does not belong to the root locus of the system is
a) -0.5
b) -2.5
c) -3.5
d) -5.5

### View Answer

Answer: c [Reason:] The points present on the root locus are right to the odd number of poles and zeroes.

4. The angles of asymptotes of the root loci of the equation s3+5s2+(K+2)s+K=0 are:
a) 0° and 270°
b) 0° and 180°
c) 90° and 270°
d) 90° and 180°

### View Answer

Answer: c [Reason:] P-Z =2 Angle of asymptote = (2q+1)180°/P-Z Angle are 90° and 270°.

5. The intersection of asymptotes of root loci of a system with open loop transfer function G(s)H(s) = K/s(s+1)(s+3) is
a) 1.44
b) 1.33
c) -1.44
d) -1.33

### View Answer

Answer: d [Reason:] The intersection of asymptotes of root loci of a system is same as the centroid which is centroid =Σreal part of open loop pole-Σreal part of open loop zeroes/P-Z. Centroid = -4/3=-1.33.

6. If a feedback control system has its open loop transfer function G(s)H(s) = K/(s-2)(s2+3s+5) has the root locus plot which intersects the imaginary axis at s =0, then the value of K at this point will be
a) -5
b) 10
c) 5
d) -10

### View Answer

Answer: b [Reason:] The intersection point on the imaginary axis at s =0 is obtained by Routh Hurwitz criteria making s^0 row zero and getting the value K = 10.

7. The open loop transfer function of the feedback control system is given by G(s) =K(s+3)/s(s+4)2(s+5)(s+6). The number of asymptotes and the centroid of asymptotes of the root loci of closed loop system is
a) 4 and (-4,0)
b) 3 and (-12,0)
c) -4 and (-4,0)
d) -3 and (-12,0)

### View Answer

Answer: a [Reason:] Number of Poles = 5 Zeroes =1 Asymptotes =P-Z =4 Centroid =Σreal part of open loop pole-Σreal part of open loop zeroes/P-Z Centroid = -4-4-5-6+3/4 =-4.

8. The characteristic equation of a control system is given as 1+ K(s+4)/s(s+7)(s2+2s+2)=0. The real axis intercept for root locus asymptote is:
a) -2.25
b) -1
c) -1.67
d) 0

### View Answer

Answer: c [Reason:] Real axis intercept =centroid Zero =-4 and Pole = -7, -1, -1, 0 Centroid =Σreal part of open loop pole-Σreal part of open loop zeroes/P-Z Centroid = -7-1-1+4/3 = -1.67.

9. The OLTF of a unity feedback system is K(s+2)(s+4)/(s+5)(s+6) the angle of arrival of the root loci as s =-2, and s =-4 respectively are:
a) 0°,180°
b) 180°,0°
c) 90°,180°
d) 180°, 90°

### View Answer

Answer: b [Reason:] As it is type zero system therefore the angle of arrival can be either 180°, 0°.

10. The characteristic equation is s3+14s2+(45+K)s+K =0, centroid is located at (-x,0) then the value of x is ____________
a) 1
b) 2
c) 3
d) 4

### View Answer

Answer: b [Reason:] Differentiating the equation of K with respect to s and equating it to zero.Breakaway points are -2, -2+1.414j,-2-j1.414. so 2 is complex breakaway point.

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