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# Multiple choice question for engineering

## Set 1

1. Consider the following statements regarding a linear discrete-time system:
H (z) = z2+1/(z+0.5)(z-0.5)
1. The system is stable
2. The initial value of h(0) of the impulse response is -4
3. The steady-state output is zero for a sinusoidal discrete time input of frequency equal to one-fourth the sampling frequency
Which of these statements are correct?
a) 1,2 and 3
b) 1 and 2
c) 1 and 3
d) 2 and 3

Answer: c [Reason:] Characteristic equation is (z+0.5) (z-0.5) =0 Its root are z =0.5, -0.5 Since both roots are inside the unit circle, hence the system is stable.

2. The minimum number of delay elements required realizing a digital filter with transfer function
H (z) =
a) 2
b) 3
c) 4
d) 5

Answer: b [Reason:] H (z) = Minimum number of delay elements= (Maximum power of z-minimum power of z) Minimum number of delay elements = 3.

3. A system can be represented in the form of state equations as:
S (n+1) =A S (n) +B x (n)
Y (n) = C S (n) +D x (n)
Where, A, B, C, D are the matrices , S(n) is the state vector , x(n) is the input and y(n) is the output . The transfer function of the system.
H (z) =Y (z)/X (z) is given by:
a) A(ZI – B)-1 C + D
b) B(ZI – C)-1 D + A
c) C(ZI – A)-1 B + D
d) D(ZI – A)-1 C + B

Answer: c [Reason:] Solving both the equations and substituting the value of the output equation into the state equation we get the value of the transfer function as obtained.

4. Assertion (A): The signals anu(n) and anu(-n-1) have the same Z transform, z/(z-a)
Reason (R): the region of convergence of anu(n) is |z|>|a|, whereas the ROC for anu(-n-1) is |z|<|a|.
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

Answer: d [Reason:] Both have the ROC as given in the reason is true but the z transform for the second is with a minus sign.

5. What is the number of roots of the polynomial F(z) = 4z3-8z2-z+2, lying outside the unit circle?
a) 0
b) 1
c) 2
d) 3

Answer: b [Reason:] Factorizing F (z) and then the factors are the roots which here come out to be 3.

6. Assertion (A): The discrete time system described by y[n] =2x[n] +4x[n-1] is unstable
Reason (R): It has an impulse response with a finite number of non-zero samples
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

Answer: d [Reason:] For the system to be stable the value of the transfer function in the discrete time domain must be summable and H[n] calculated is summable hence the system is stable.

7. What is the z-transform of the signal x[n] = anu(n)?
a) X(z) =1/z-1
b) X(z) = 1/1-z
c) X(z) = z/z-a
d) X(z) = 1/z-a

Answer: c [Reason:] By definition this is the basic example of the z-transform and the Z-Transform of the equation is calculated is z/z-a.

8. Which one of the following rules determine the mapping of s-plane to z-plane?
a) Right side of the s-plane maps into outside of the unit circle in z-plane
b) Left half of s-plane maps into inside of the unit circle
c) Imaginary axis in s-plane maps into the circumference of the unit circle
d) All of the mentioned

Answer: d [Reason:] S- plane can be mapped into the z plane with certain rules than right side maps into the outside, left side maps into the inside and imaginary axis maps on the unit circle of the z plane.

9. Assertion (A): The z-transform of the output of the sampler is given by the series.
Reason (R): The relationship is the result of the application of z = e-sT, where T stands for the time gap between the samples.
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

Answer: c [Reason:] T is termed as the time of the sampling instant and z transform is always defined for the instant of the sampling event and this can be as desired by the user.

10. Convolution of two sequences X1[n] and X2[n] are represented by:
a) X1(z)*X2(z)
b) X1(z)X2(z)
c) X1(z)+X2(z)
d) X1(z)/X2(z)

Answer: a [Reason:] Convolution of the two sequences is the combination of multiplication and addition of the two sequences at each instant and convolution in time domain is multiplication in the frequency domain.

## Set 2

1. The discrete-time signal x (n) = (-1)n is periodic with fundamental period
a) 6
b) 4
c) 2
d) 0

Answer: c [Reason:] Period of the signal refers to the instant of time at which the signal repeats itself and for this Period =2 of the given discrete time signal.

2. The frequency of a continuous time signal x (t) changes on transformation from x (t) to x (α t), α > 0 by a factor
a) α
b) 1/α
c) α2
d) α

Answer: a [Reason:] x(t)->x(αt), α > 0 α > 1 compression in t, expansion in f by α. α < 1 expansion in t, compression in f by α.

3. Two sequences x1 (n) and x2 (n) are related by x2 (n) = x1 (- n). In the z- domain, their ROC’s are
a) The same
b) Reciprocal of each other
c) Negative of each other
d) Complements of each other

Answer: b [Reason:] x1(n) is the signal in the discrete domain and X1(z) is the signal in the z domain, RoC Rx z Reciprocals x2(n) = x1(-n) X1(1/z), RoC 1/ Rx

4. The ROC of z-transform of the discrete time sequence x(n) = is:
a) 1/3>|z|<1/2
b) |z|>1/2
c) |z|<1/3
d) 2>|z|<3

Answer: a [Reason:] One part of the equation is the right sided signal and other part is the left sided signal hence the ROC of the system will be 1/3>|z|<1/2.

5. Which one of the following is the correct statement? The region of convergence of z-transform of x[n] consists of the values of z for which x[n] is:
a) Absolutely integrable
b) Absolutely summable
c) Unity
d) <1

Answer: b [Reason:] The region of convergence of z-transform of x[n] consists of the values of z for which x[n]r-n is absolutely summable.

6. The region of convergence of the z-transform of a unit step function is:
a) |z|>1
b) |z|<1
c) (Real part of z)>0
d) (Real part of z)<0

Answer: a [Reason:] h[n] =u[n] Hence, Region of Convergence is the region for which the values of the roots in z transform are lying in the function and is the range of values of z for which |z|>1.

7. If the region of convergence of x1[n]+x2[n] is 1/>|z|<2/3, the region of convergence of x1[n]-x2[n] includes:
a) 1/3>|z|<3
b) 2/3>|z|<3
c) 3/2>|z|<3
d) 1/3>|z|<2/3

Answer: d [Reason:] Region of Convergence is the region for which the values of the roots in z transform are lying in the function and ROC remains the same for addition and subtraction in z-domain.

8. A sequence x (n) with the z-transform X (z) = Z4 + Z2 – 2z + 2 – 3Z-4 is applied to an input to a linear time invariant system with the impulse response h (n) = 2δ (n-3). The output at n = 4 will be:
a) -6
b) Zero
c) 2
d) -4

Answer: b [Reason:] H (z) = 2z-3 Then taking the inverse Laplace transform of the equation of Y (z) at n=4 y(n) =0.

9. H (z) is discrete rational transfer function. To ensure that both H(z) and its inverse are stable:
a) Poles must be inside the unit circle and zeros must be outside the unit circle
b) Poles and zeroes must be inside the unit circle
c) Poles and zeroes must be outside the unit circle
d) Poles must be outside the unit circle and zeros must be inside the unit circle

Answer: b [Reason:] For H(z) to be stable the poles must be inside the unit circle and for the inverse of H(z) to be stable the poles of it must be inside the unit circle.

10. Z and Laplace transform are related by:
a) s = ln z
b) s =ln z/T
c) s =z
d) s= T/ln z

Answer: b [Reason:] z = est s =ln z/T.

## Set 3

1. The DFT of a signal x(n) of length N is X(k). When X(k) is given and x(n) is computed from it, the length of x(n)
a) Is increased to infinity
b) Remains N
c) Becomes 2N – 1
d) Becomes N2

Answer: a [Reason:] When X (k) is given and x (n) is computed from it, the length of x (n) is increased to infinity.

2. The system having input x (n) related to output y(n) as y (n) = log |x (n)| is:
a) Nonlinear, causal, stable
b) Linear, noncausal, stable
c) Nonlinear, causal, not stable
d) Linear, noncausal, not stable

Answer: a [Reason:] As y (n) is the function of x (n) hence it is nonlinear but it is bounded and also depends upon past and present values therefore it is stable and causal respectively.

3. Zero-order hold used in practical reconstruction of continuous-time signals is mathematically represented as a weighted-sum of rectangular pulses shifted by:
a) Any multiples of the sampling interval
b) Integer multiples of the sampling interval
c) One sampling interval
d) 1 second intervals

Answer: b [Reason:] Zero-order hold is used to reconstruct the continuous-time signal which is represented as a weighted sum of rectangular pulses shifted by integer multiples of the sampling interval.

4. When two honest coins are simultaneously tossed, the probability of two heads on any given trial is:
a) 1
b) 3/4
c) 1/2
d) ¼

Answer: d [Reason:] Total outcomes =4 Favorable outcomes =1 Hence probability =1/4.

5. A continuous-time periodic signal x(t), having a period T, is convolved with itself. The resulting signal is
a) Not periodic
b) Periodic having a period T
c) Periodic having a period 2T
d) Periodic having a period T/2

Answer: b [Reason:] Periodic having a period T Convolution of a periodic signal (period T) with itself will give the same period T.

6. If the Fourier series coefficients of a signal are periodic then the signal must be
a) Continuous-time, periodic
b) Discrete-time, periodic
c) Continuous-time, non-periodic
d) Discrete-time, non-periodic

Answer: b [Reason:] Discrete-time, periodic these are the properties of the discrete-time periodic signal.

7. The region of convergence of a causal finite duration discrete-time signal is
a) The entire z-plane except z = 0
b) The entire z-plane except z = ∞
c) The entire z-plane
d) A strip in z-plane enclosing jω–axis

Answer: a [Reason:] For discrete time signal for any causal system the region of convergence is always entire z-plane but except z =0.

8. The probability cumulative distribution function must be monotone and
a) Increasing
b) Decreasing
c) Non-increasing
d) Non-decreasing

Answer: d [Reason:] The cumulative distribution function that is monotone and non-decreasing or can be increasing.

9. Convolution is used to find:
a) The impulse response of an LTI System
b) Frequency response of a System
c) The time response of a LTI system
d) The phase response of a LTI system

Answer: c [Reason:] Convolution is the combination of addition and multiplication of the signals and used to find the impulse response of the LTI system.

10. The Fourier Transform of a rectangular pulse is
a) Another rectangular pulse
b) Triangular pulse
c) Sinc function
d) Impulse

Answer: c [Reason:] The Fourier Transform of a rectangular pulse that is the sinc function.

## Set 4

1. The most important consideration for designing of control system are:
a) Transient response measures
c) Temporary response
d) Final response

Answer: c [Reason:] The important point to keep in mind for designing control system are the transient response and steady state response as for designing a control system both of the responses are used in detail. .

2. Steady state error is usually specified in terms of :
a) Error constants
b) Damping factor
c) Speed of response
d) Bandwidth

Answer: a [Reason:] Steady state error is the error that is specified as the time approaches infinite and value approaches the final value and specified mainly in terms of error constants that are mainly position, velocity and acceleration error constants.

3. Transient response measure is usually specified in terms of :
a) Error constants
b) Damping factor
c) Speed of response
d) Both b and c

Answer: d [Reason:] Transient response is the response taken at any particular time during analysis and that is mainly specified in terms of damping factor and speed of response that is mainly settling time and rise time.

4. In time domain the measure of relative stability is:
a) Damping factor
b) Maximum peak overshoot
c) Damping factor and Maximum peak overshoot
d) Speed of response

Answer: c [Reason:] Relative stability is the measure of stability of a particular control system with respect to some reference and is measured both in time and frequency domain as in time domain it is the measure of damping factor and maximum peak overshoot.

5. In frequency domain the measure of relative stability is:
a) Resonant peak
b) Phase margin
c) Resonant peak and phase margin
d) Maximum peak overshoot

Answer: c [Reason:] Relative stability is the measure of stability of a particular control system with respect to some reference and is measured both in time and frequency domain as in frequency domain it is the measure of both resonant peak and phase margin.

6. In time domain the speed of response is measured in terms of :
a) Rise time
b) Settling time
c) Natural frequency
d) All of the mentioned

Answer: d [Reason:] The value of rise time must be less so that the speed of response of control system must be large and it depends upon the rise time, settling time and natural frequency.

7. In frequency domain the speed of response is measured in terms of:
a) Resonant frequency
b) Bandwidth
c) Resonant peak and bandwidth
d) Maximum peak overshoot

Answer: c [Reason:] The speed of response is the time to get the final response and in frequency domain it depends upon the resonant frequency the frequency at which the resonant peak is obtained and bandwidth.

8. The compensator for the system can be:
a) Electrical
b) Mechanical
c) Hydraulic
d) All of the mentioned

Answer: d [Reason:] Compensator can be of any different type but mainly electric network serves as the compensator.

9. The compensator transfer function can be placed in:
b) Feedback or parallel compensation
c) Positive
d) Negative

Answer: c [Reason:] Compensator are the devices used in frequency domain so as to get the desired response and there are various methods to place the compensators in the system as cascade or series or feedback or parallel.

10. Lead compensator speeds up the transient response and increases the margin of stability of a system.
a) True
b) False

Answer: a [Reason:] Derivative compensation are also known as the lead compensators are these make the speed of response of the system more and also the bandwidth and hence make the system more stable.

## Set 5

1. If the speed of rotation of a separately excited dc machine is halved and the filed strength is also reduced to half of the original. Then the emf induced in the armature
a) reduces to 1/4th of original
b) reduces to half of original
c) remains same
d) doubles

Answer: a [Reason:] Emf is proportional to speed of rotation and flux.

2. If the speed of rotation for a four pole, 220V dc machine is 1 m/s, flux density as 2T having length of bore as 0.1m and radius of 0.5m.
The emf induced under pole faces will be
a) 0.2 V
b) 0.1 V
c) 0.2*pi V
d) 220 V

Answer: a [Reason:] E = B*l*v = 2*0.1*1 = 0.2 Volts.

3. The induced emf in the armature of a 4-pole dc machine is
a) directly proportional to speed and field strength applied to it
b) directly proportional to speed
c) directly proportional to field strength applied to it
d) inversely proportional to speed and inversely proportional to field strength applied to it

Answer: a [Reason:] Emf is proportional to speed of rotation and flux.

4. If the armature current is by mistake increased to 50% for the dc machine,
a) then the induced emf remains unchanged
b) then the induced emf doubles
c) then the induced emf halves
d) none of the mentioned

Answer: a [Reason:] Emf is proportional to speed of rotation and flux.

5. For a four pole, 16 slot armature with two coil-side/slot having lap connected progressive winding has single turn coils. The same machine is then wave wound, the emf induced in the lap wound dc machine to that of wave wound will be
a) 2
b) 0.5
c) 1
d) 4

Answer: b [Reason:] E=1/(P/2) =1/(4/2) = 1/2 V.

6. A duplex lap wound armature is used in six pole dc machine with six brush set. The number of current paths in this machine is
a) 12
b) 6
c) 3
d) 2

Answer: a [Reason:] The number of parallel paths for a lap wound machine is number of parallel paths. As it is a duplex winding, it will have 6*2 = 12 parallel paths.

7. For a four pole, 16 slot armature with two coil-side/slot having wave connected progressive winding has single turn coils has simplex winding.
The number of current paths
a) 2
b) 6
c) 3
d) 4

Answer: a [Reason:] The number of parallel path for a wave wound machine is equal to two.

8. For a four pole, 200 V dc shunt generator having armature resistance of 1 ohms. The current flowing in the armature is 10 A. What is the back emf generated if the terminal voltage of 220 V supply is fed?
a) 230 Volts
b) 210 Volts
c) 190 Volts
d) 200 Volts

Answer: a [Reason:] E=V+I*ra = 220+10*1 =230 Volts.

9. For a 4 pole 200 V, 20 A dc generator running at the rated rpm with no load will be
b) 4000 W no load losses
d) none of the mentioned

Answer: a [Reason:] As there is no load and assuming no armature resistance, the no load losses should ideally be zero.

10. Which of the following cannot reduce the terminal voltage of a dc shunt generator?
a) Commutation
b) Armature reaction
c) Armature ohmic losses
d) Any of the mentioned