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Q.P. Code :36273

Turn Over

[Time: 3 Hours] [ Marks:80]

Please check whether you have got the right question paper.

N.B: 1. Question No. 1 is compulsory.

2. Attempt any three from remaining five questions.

3. Assume suitable data if any required.

Q.1 Answer the following (any four)

a) What is the principle of argument.

b) What are the frequency domain specification.

c) Explain regenerative feedback.

d) Explain the standard signal.

e) Explain the stability criteria on polar plot.

20

Q.2 a) Sketch the root locus plot for the system with open loop transfer function.

𝐺 (𝑠)𝐻(𝑠) =𝐾

(𝑆+1 )(𝑆2+4𝑆+13) . also find maximum value of K for stability.

b) Derive the output equation for the second order system to the unit step input also draw the

unit steep response curves for different values of damping factor ‘𝜉’

10

10

Q.3 a) Obtain a transfer function using Mason’s gain formula.

b) Sketch the bode plot and determine Wgc, Wpc, gain margin and phase margin.

100( )

2 20G s

s s s

10

10

Paper / Subject Code: 39501 / FEEDBACK CONTROL SYSTEM

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Q.P. Code :36273

Turn Over

2

Q.4 a) Sketch the polar plot for unity feedback closed loop system. 𝐺 (𝑠) =1

𝑆 (𝑆+1)2

b) Find the transfer function 𝑥2(𝑠)

𝐹(𝑠) of the given system.

10

10

Q.5 a) The open loop transfer function of a feedback control system is

𝐺 (𝑠)𝐻 (𝑠) =𝐾

𝑆 (𝑆2+2𝑆+2 ) (𝑆+4)

1) Using routh array criterion, determine range of value of K for which system is stable

2) If the zero at 𝑧 = −4 is added to forward path transfer function how is stability

affected.

b) Unity feedback system has a transfer function 𝐺 (𝑠) =2𝑆

𝑆(𝑆+5) determine damping ratio,

peak overshoot, Rise time and settling time.

10

10

Q.6 a) For system shown in figure, find the error using dynamic error coefficient method for

input of 6 + 5𝑡 +6𝑡2

2 .

b) What do you mean by angle of arrival? How do you determine it.

c) State and explain Nyquist stability theorem.

10

05

05

------------------------

Paper / Subject Code: 39501 / FEEDBACK CONTROL SYSTEM

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Page 1 of 2

56504

Duration: 3 Hours Marks: 80

N.B: a) Question number 1 is compulsory

b) Solve any three from the remaining.

c) All the question carry equal marks

1. a) Find the extremal of ∫1+𝑦2

𝑦′2𝑑𝑥

𝜋

0 subject to 𝑦(0) = 0 , 𝑦(𝜋) = 0 . [5]

b) Using Cauchy’s Schwartz Inequality, show that (𝑎𝑐𝑜𝑠𝜃 + 𝑏𝑠𝑖𝑛𝜃)2 ≤ 𝑎2 + 𝑏2,

Where ‘a’ and ‘b’ are real. [5]

c) Show that Eigen values of Hermitian matrix are real. [5]

d) Evaluate ∫(𝑧2 − 2𝑧 + 1) 𝑑𝑧 over a closed circle 𝑥2 + 𝑦2 = 2. [5]

2. a) Find the extremal ∫ (𝑦2 − 𝑦′2− 2𝑦𝑐𝑜𝑠ℎ𝑥)𝑑𝑥

𝑥2

𝑥1 [6]

b) Find the Eigen values and Eigen Vectors of the matrix 𝐴2 + 3𝐼, where [6]

𝐴 = [8 −6 2

−6 7 −42 −4 3

]

c) Obtain all possible expansion of 𝑓(𝑧) =1

𝑧2(𝑧−1)(𝑧+2) about 𝑧 = 0 indicating

region of convergence. [8]

3. a) Verify Cayley - Hamilton Theorem for 𝐴 = [1 −1 02 3 −2

−2 0 1] and find 𝐴−1. [6]

b) b) Using Residue theorem evaluate

C

z

dzz

e

22

where C is |z|=4. [6]

c) Show that a closed curve ‘C’ of a given fixed length (perimeter) which encloses

maximum area is a circle. [8]

4. a) Find an orthonormal basis for the subspace of 𝑅3 by applying Gram-Schmidt

process, where 𝑢1 = (1,0,0), 𝑢2 = (3,7, −2), 𝑢3 = (0,4,1). [6]

b) Find 𝐴50 for the matrix 𝐴 = [4 37 8

] [6]

Paper / Subject Code: 39002 / APPLIED MATHEMATICS - IV

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Page 2 of 2

56504

c) Reduce the Quadratic Form 𝑥𝑦 + 𝑦𝑧 + 𝑧𝑥 to normal form by congruent

transformation. [8]

5. a ) Using Rayleigh-Ritz Method, find an approximate solution to the extremal problem

∫ (𝑦2 + 2𝑦𝑥−𝑦′2)𝑑𝑥

1

0, 𝑦(0) = 0, 𝑦(1) = 0. [6]

b) Determine whether the set 𝑉 = (𝑥, 𝑦, 𝑧): 𝑥 = 1, 𝑦 = 0 𝑜𝑟 𝑧 = 0 is a subspace

of 𝑅3 [6]

c) Show that the matrix 𝐴 = [8 −6 2

−6 7 −42 −4 3

] is diogonable.Also find the transforming

matrix and diagonal matrix. [8]

6. a) Using Cauchy’s Residue Theorem, evaluate ∫𝑑𝜃

2+ 𝐶𝑂𝑆𝜃

2𝜋

0 [6]

b) Evaluate ∫ (2𝑥 + 1 + 𝑖𝑦)𝑑𝑧2+𝑖

1−𝑖 along the straight line joining 𝐴(1, −1) 𝑎𝑛𝑑

𝐵(2,1) [6]

c) Find the singular value decomposition of the matrix A= [2 30 2

] [8]

****************

Paper / Subject Code: 39002 / APPLIED MATHEMATICS - IV

FE0BAE96CD978645FF710C55C00FB300

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Q. P. Code: 13788

Three Hours Total Marks: 80

N.B. 1) Question No. 1 is compulsory.

2) Attempt any THREE questions from the remaining five questions.

3) Assume suitable data if necessary and mentioned it.

Q.1) Attempt any Four 20

a) What are the various torques required in measuring instruments?

b) Define i) Back EMF, ii) Slip.

c) Why single phase induction motor is not self starting?

d) Derive the basic balance bridge equation.

e) Why DC series motor should not be started at NO LOAD condition?

Q.2) a) Explain the characteristics of DC shunt and DC series motor. 10

b) With neat diagrams explain production of ‘Rotating Magnetic Field’ in

3 phase induction motor. 10

Q.3) a) What is necessity of starter in DC motor? Explain 3 Point Starter. 10

b) How the Kelvin Double Bridge is use as low value resistance measurement? 10

Q.4) a) Write note on i) DVM and ii) DMM 10

b) Explain construction and working of PMMC instruments 10

Q.5) a) Star connected rotor of an 3 phase induction motor has a standstill impedance of

(0.4 + j4) ohm/phase and rheostat impedance /phase is (6 + j2) ohm. The motor has an

Induced emf of 80V between slip rings at standstill when connected to its normal

supply voltage. Find rotor current i) at standstill with rheostat is in circuit.

ii) When slip rings are short circuited and motor is running with slip of 3%. 10

b) Explain speed control methods of 3 phase induction motor. 10

Q.6) a) Explain any one type of ADC 10

b) Explain working of Q - meter. 10

--------------------

Paper / Subject Code: 39503 / ELECTRICAL TECHNOLOGY & INSTRUMENTS

006FBA1142B8E6298C01453C505E1041

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59606 Page 1 of 1

(3 Hours) [Total Marks : 80]

N.B. : (1) Question No. 1 is compulsory.

(2) Attempt any three questions from the remaining five questions.

(3) Assume suitable data if necessary.

1. Attempt any four :- 20

(a) Explain OSI reference model.

(b) Explain FM Noise Triangle.

(c) Compare QPSK and QAM.

(d) Write note on PAM telemetry system.

(e) Compare the SSB and VSB techniques.

2. (a) Draw the ASK,BPSK,QPSK waveforms for digital data 101001100. 10

(b) With the help of neat block diagram explain the principle and generation

of Armstrong method of FM generation. 10

3. (a) Explain various noise sources that affect communication and also

derive friss formula for total noise factor. 10

(b) A radio receiver with 22 KHz bandwidth has a noise figure of 25 dB.

Determine the signal power required at the input of receiver to achieve

input SNR of 41 dB. 10

4. (a) Explain Delta modulation transmitter and receiver system with neat sketch. 10

(b) Explain the various communication modes as simplex, half duplex and

duplex in detail. 10

5. (a) Explain in brief :- 10

(i) Pulse Amplitude Modulation.

(ii) Pulse Width Modulation.

(b) With the help of neat sketches explain voltage and current telemetry Systems. 10

6. Write Short notes on any two :- 20

(a) Frequency Shift Keying (FSK).

(b) Feedback Telemetry.

(c) Adaptive Delta Modulation technique.

******************

Paper / Subject Code: 39504 / COMMUNICATION SYSTEM

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68669 Page 1 of 1

[Time: Three Hours] [ Marks:80]

N.B: 1. Question.No.1 is compulsory.

2. Attempt any three questions from remaining five questions.

3. Assume suitable data wherever necessary.

1 Attempt the following. 20

a Explain different types of strain gauges.

b What is Vena contracta? State and explain types of fluid flow.

c What are the different methods of humidity measurement? Explain any one of them.

d Explain any one method for force measurement.

2 a Explain with diagram working of Pirani Gauge. 10

b A strain gauge bonded to a steel beam 0.1 m long and has a crossectional area 4 cm2.Young’s

modulus for steel is 207 GN/m2.The strain gauge has an unstrained resistance of 240Ω and

gauge factor of 2.2.When a load is applied, the resistance of gauges changes by

0.013Ω.Calculate the change in length of the steel beam and an amount of force applied to the

beam.

10

3 a Explain with diagram calibration procedure of pressure gauges using Dead Weight Tester. 10

b What is ORP? Explain setup used for ORP measurement. 10

4 a Classify flow measurement techniques .Explain the construction and working of

electromagnetic flow meter.

10

b Draw and explain pressure measurement scheme using LVDT. 10

5 a State and derive Bernoulli’s equation. 10

b Draw and explain PH set up along with its different electrodes. 10

6 a What are the different methods of Viscosity measurement? Explain any one of them. 10

b Compare orifice and venturi meter. 10 _________________________

Paper / Subject Code: 39505 / TRANSDUCERS - II

C6948EF61F21F6B48B0080F3BE39ED9D