discrete mathematical structures - vardhaman · :: 2 :: 8. a) explain the structures and operations...

Hall Ticket No: Question Paper Code: A1505

(AUTONOMOUS) B. Tech III Semester Supplementary Examinations, November - 2017

(Regulations: VCE-R11/R11A)

DISCRETE MATHEMATICAL STRUCTURES

(Common to Computer Science and Engineering & Information Technology)

Date: 13 November, 2017 FN Time: 3 hours Max Marks: 75

Answer ONE question from each Unit All Questions Carry Equal Marks

Unit – I

1.

a) Prove or disprove p p q q is a contingency using a truth table.

7M

b) By using logic equivalence, prove or disprove ( p (p q)) q T .

8M

2. a) Obtain the principal disjunctive normal form of P Q P R Q R using

the truth table.

7M

b) Suppose you have predicates A(x), E(x) and W(x). Negate the following logical statements and then push all negations inward so that they are only acting on

predicates. For example, if you are given x E (x), negate it as ¬( x E(x)). Then push in the negation getting ¬E(x). Also, state whether the statement is a predicate or a proposition. You may assume that the domain of discourse is the same for the three predicates A(x),E(x),and W(x). (you also need to use A(x)→E(x)≡¬A(x) E(x) to push in negations on implications).

8M

Unit – II

3. a) i. Find the range of f(x), where f(x): R → R and f (x) = x2 / (x2 + 1). ii. Draw a Hasse diagram for (A, divisibility relation), where:

I. A = 1, 2, 3, 4, 5, 6, 7, 8 II. A = 1, 2, 3, 5, 11, 13 III. A = 2, 3, 4, 5, 6, 30, 60 IV. A = 1, 2, 4, 8, 16, 32, 64 V. A = 1, 2, 3, 6, 12, 24 VI. A = 2, 4, 6, 12, 24, 36

10M

b) The following arrays describe a relation R on the set A = 1, 2, 3, 4, 5, 6,.7, 8, 9, 10 Compute both the digraph of R and the matrix M. i. VERT=(6, 2), (8,7),(10, 2) ii. TAIL=(2, 2), (1, 1), (4, 3), (4, 5) iii. HEAD=(4, 3), (5,1), (2, 3), (5, 4), (2, 4) iv. NEXT=(3, 1), (4, 10), (10, 5), (9, 10), (10,10)

5M

4. a) Given A=2, 3, 4, B = 2, 5, 6, 7. Construct examples of each of the following: i. All injective mappings from A to B ii. All surjetive mappings from A to B which is not injective iii. All bijective mappings from B to A

7M

b) Let R be relation defined on the set of natural number N as follows: R=(x, y): x N,y N, 2x+y=41 Find the domain and range of the relation R. Also, verify whether R is reflexive, symmetric and transitive.

8M

Cont…2

:: 2 ::

Unit – III

5. a) Define the following and give suitable examples for each: i. Lattice ii. Sub lattice iii. Distributive lattice iv. Complemented lattice

7M

b) Let n be a positive integer and Sn be the set of all divisors of n. let D denote the relation of “division”. Draw the diagrams of lattices (Sn, D) for n=6, 8, 24 and 30.

8M

6. a) State and prove the distributive inequalities in lattices. 8M b) Let S1=p, q, r and A is its power set. The partially ordered set ,S is a lattice

in which the meet and join are the usual operations of intersection and union respectively. Draw the diagram for the lattice , ,S

7M

Unit – IV

7. a) There are 30 females and 35 males in the junior class while there are 25 females and 20males in the senior class. In how many ways can a committee of 10 be chosen so that there are exactly 5 females and 3 juniors on the committee?

7M

b) How many ways are there to select 2 cards (without replacement) from a deck of 52? How many ways are there to select the 2 cards such that: i. The first card is an ace and the second card is a king ii. The first card is an ace and the second is not a king iii. The first card is a heart and the second is a club iv. The first card is a heart and the second is a king v. The first card is a heart and the second is not a king

8M

8. a) Determine the coefficients of: i. x5y2 in the expansion of (2x-3y)7 ii. p2q3r2s5 in the expansion of (p+2q-3r+2s+5)16 iii. Find the number of terms in expansion of (a+3b-4c+2d)12

9M

b) From a group of 10 professors how many ways can a committee of 5 members be formed so that at least one of Professor A and Professor B will be included.

6M

Unit – V

9.

a) Solve the recurrence relation ( 1) 3n

n na a where 0 1a by substitution method.

7M

b) Solve the recurrence relation using generating functions

1 2 39 26 24 0n n n na a a a where 0 1 20, 1, 10a a a .

8M

10. a) Find the solution of the recurrence relation using characteristic roots

1 2 37 16 12 0n n n na a a a where 0 1 21, 4, 8.a a a

8M

b) Find a particularsolution to the following inhomogeneous recurrence relation

1 25 6 2 2n

n n na a a for n .

7M



(Regulations: VCE-R14)

OPERATING SYSTEMS




Unit – I

1. a) Explain any two operating system structures with neat diagrams. 5M b) Distinguish between multiprogramming and multitasking operating systems. Explain the

operating system services that are helpful for the users.

10M

2. a) Mention operating system activities with respect to process management and memory management.

6M

b) Differentiate between system calls and system programs. Briefly explain the two models of inter process communication.

9M

Unit – II

3. a) Explain different multithreading models. 7M b) Consider the following processes with their CPU burst times given in milliseconds. Process

is arrived in P1, P2, P3, P4, P5 order of all at time 0.

Process Burst Time Priority

P1 10 3

P2 1 1

P3 2 3

P4 1 4

P5 5 2

Write the Gantt chart, calculate the average waiting time for FCFS, and Round robin (time quantum=1ms).

8M

4. a) State dining philosopher’s problem and give solution using monitors. 8M b) Describe ‘Test-and-Set’ and ‘Swap’ instructions and their use in synchronization of

processes.

7M

Unit – III

5. a) What do you mean by deadlock avoidance? Write and explain the safety and resource request algorithm.

10M

b) Distinguish between paging and segmentation. 5M 6. a) Consider the following page reference string 0123012301234567. How many page faults

would occur in case of frame size of 3: i. FIFO ii. LRU iii. Optimal iv. LFU

8M

b) Explain how deadlocks can be prevented by denying circular wait and no pre-emption.

7M

Unit – IV

7. a) Identify and explain different access methods on files. 6M b) Identifying the issues that arise when multiple users share files, explain how file sharing

can be extended to multiple file systems and remote file systems.

9M

Cont…2

:: 2 ::

8. a) Explain the structures and operations used to implement file system operations. 9M b) Suppose that a disk drive has 5000 cylinders, numbered 0 to 4999. The drive is currently

serving a request at cylinder 143, and the previous request was at cylinder 125. The queue of pending requests, in FIFO order is: 86, 1470, 913, 1774, 948, 1509, 1022, 1750, 130 Starting from the current head position, what is the total distance that the disk arm moves to satisfy all the pending requests for each of the following disk-scheduling algorithms: i. FCFS ii. SSTF iii. SCAN

6M

Unit – V

9. a) With a neat diagram, explain encryption and decryption using RSA asymmetric cryptography.

10M

b) Explain how a firewall can be used to protect the system.

5M

10. a) Differentiate between viruses and worms. 5M b) What do you mean by access matrix? Discuss the various methods of implementing

access matrix. 10M



(Regulations: VCE-R11/11A)

DATA STRUCTURES THROUGH C (Mechanical Engineering)



Unit – I

1. a) What is an algorithm? List the characteristics of an algorithm. 8M b) Write an algorithm to implement linear search.

7M

2. a) Define recursion. Write an algorithm to find the GCD of given three numbers. 7M b) Write an algorithm to implement Fibonacci search.

8M

Unit – II

3. Write the algorithm for Bubble and insertion sort. Explain their best case and worst case complexities.

15M

4. Explain the following: i. Merge sort ii. Radix sort

15M

Unit – III

5. a) List the differences between stack and queue. 8M b) What is dequeue? What are the different operations can be performed on

dequeue? What is the need of dequeue?

7M

6. a) Write algorithms that reverse all the elements in a queue. 7M b) Translate infix expression into its equivalent post fix expression:

A*(B+D)/E-F*(G+H/K) (A+B^D)/(E-F)+G

8M

Unit – IV

7. a) What is linked list? List the advantages and disadvantages of linked list. 5M b) Explain single linked list insertion and deletion algorithms with example.

10M

8. a) List the applications of single linked list. 5M b) Write an algorithm to merge two single linked lists into one list.

10M

Unit – V

9. a) Define the following and also provide examples for each: i. Binary trees ii. Complete Binary trees iii. Full Binary trees iv. Binary search tree

8M

b) Write a C program to create and display Binary search tree.

7M

10. a) Write C routines to traverse the binary trees in in-order, pre-order and post-order.

7M

b) Explain DFS with algorithm and an example. 8M




COMPUTER ARCHITECTURE AND ORGANIZATION

(Information Technology)



Unit – I

1. a) Which are the functionally independent parts of a computer? Explain with the help of a diagram.

7M

b) Convert the following numbers to binary: i. (0.625)10 ii. (673)8 iii. (17.625)10 iv. (F3A7C2)16

8M

2. a) Explain how error detection is done using parity. 8M b) List out the parameters used for measuring the performance of a computer. Explain the

terms involved and basic performance equation.

7M

Unit – II

3. a) Describe the Basic computer instruction formats with example. 7M b) Define the sequence of micro operations to be performed for push and pop operations

and also Explain the organization of register stack.

8M

4. a) With a flowchart explain how interrupts are handled by computer. 7M b) Illustrate with example any four Memory Reference instructions.

8M

Unit – III

5. a) With a neat diagram, explain the micro programmed control unit. 10M b) Divide 17 by 5 using restoring division techniques.

5M

6. a) Explain the floating point addition/subtraction unit. 10M b) What are the address sequencing capabilities required in a control memory?

5M

Unit – IV

7. a) What do you mean by direct memory access? Explain. Differentiate between burst mode DMA and cycle stealing DMA.

10M

b) Write a note on pipelining.

5M

8. a) Define parallel processing. Explain flynns classification of computers. 10M b) With a timing diagram, explain how input operation takes place using synchronous

bus.

5M

Unit – V

9. a) Explain the characteristics of multiprocessor systems. 10M b) Differentiate between synchronous and asynchronous bus.

5M

10. a) Explain the following interconnection networks in detail. i. Time shared common bus ii. Hypercube system

10M

b) Discuss some solutions to the cache coherence problem. 5M




OBJECT ORIENTED PROGRAMMING THROUGH JAVA




Unit – I

1. a) What is the use of ‘this’ keyword in Java? Bring out the significance of using ‘this()’ in constructor overloading with a suitable example.

8M

b) Describe the features/buzzwords of Java programming language.

7M

2. a) Discuss the need for object oriented paradigm and its features. 8M b) Design a java program to demonstrate types of constructors in java.

7M

Unit – II

3. a) What is inheritance? Explain the types of inheritance supported by java. 10M b) What is interface? Can interface be extended? Give an example.

5M

4. a) Illustrate the concept “Dynamic method dispatch” with a suitable example program. 8M b) Explain the ‘final’ keyword usage in java. 7M

Unit – III 5. a) i. What are the states/lifecycle of a thread? Explain with a neat diagram

ii. Differentiate between Error and Exception 8M

b) Write a java program to create multiple threads.

7M

6. a) Explain thread priority. Write a program to demonstrate getPriority() and setPriority() methods.

7M

b) Discuss the exception handling mechanism in Java.

8M

Unit – IV

7. a) Design a Java program to implement a frame window using AWT components. 8M b) Is it possible to create a set of mutually exclusive check boxes in which one and only

one check box in the group can be checked at any one time? Justify your answer.

7M

8. a) Discuss the delegation event model in Java. 8M b) List the types of Layout Managers in Java. Describe any three of them.

7M

Unit – V

9. a) Differentiate between AWT and Swings. 7M b) Write a program to demonstrate passing parameters to Applets.

8M

10. a) Outline any five attributes of the HTML APPLET Tag. 6M b) With a neat diagram, explain the life cycle of Applets. 9M




ELECTRONIC DEVICES

(Electronics and Communication Engineering)



Unit – I

1. a) Derive an expression for the electron current due to drift and diffusion. 8M b) The intrinsic carrier concentration for silicon at room-temperature (3000K) is

1.5x1010/cm3. If the mobility’s of electrons and holes are 1300cm2/Vs and 450cm2/Vs respectively, what is the conductivity of silicon (intrinsic) at 3000K? If silicon is doped with 1018 boron per cm3, what is its conductivity?

7M

2. a) Find the conductivity and resistivity of an intrinsic semiconductor at temperature of 3000K k. It is given that ni=2.5x1013/cm3, n=3,800cm2/Vs, p=1,800cm2/ Vs e=1.6x10-19

C.

7M

b) Define Hall Effect in semiconductor? The resistivity of doped silicon material is

9x10-3 -m. The Hall co-efficient is 3.6x10-4 m3 coulomb-1. Assuming single carrier conduction, find the mobility and density of charge carriers e=1.6x10-19 coulombs.

8M

Unit – II

3. a) Show that the reverse saturation current doubles for every 010 C rise in temperature for a diode.

8M

b) A silicon diode has a reverse saturation current of 7.12 n A at room temperature of027 C . Calculate its forward current if it is baised with a voltage of 0.7V .

7M

4. a) Describe transition and diffusion capacitance of a diode with neat diagram. 7M b) Explain the equivalent circuits of a diode with proper approximation.

8M

Unit – III

5. a) Briefly explain the principle of operation of a LED. 6M b) Derive the ripple factor and efficiency for the half-wave rectifier. 9M 6. a) Write short notes on:

i. Photodiodes ii. Varactor diode

6M

b) Draw the circuit and explain the working of a bridge rectifier. Why it is preferred over a full-wave rectifier.

9M

Unit – IV

7. a) Draw the structure of a JFET and explain its principle of operation with neat diagrams along with its V-I characteristics.

8M

b) Draw the circuit of transistor in the common emitter configuration. Sketch the input and output characteristics.

7M

8. a) With the help of neat sketch, explain the operation and construction of enhancement type of N-Channel MOSFET.

7M

b) Draw the two transistor analogous circuit of an SCR and explain its operation. Sketch its V-I characteristics.

8M

Cont…2

:: 2 ::

Unit – V

9. a) Explain the effect of variation in base current on Q-point in the load line analyze of the fixed bias circuit.

7M

b) For a fixed bias circuit shown in Fig.1, assuming 0.7BEV V and 60 find:

i. Quiescent values of base and collection currents ii. Quiescent value of VCE iii. Base ground and collection – ground voltages iv. Base collector voltage

Fig.1

8M

10. a) With diagram explain the self bias configuration of JFET. 7M b) For the circuit shown in Fig.2, determine:

i. IB & IC ii. VCE and VC iii. VE & IC sat

Fig.2

8M




ELEMENTS OF ELECTRICAL ENGINEERING (Common to Computer Science and Engineering & Information Technology)



Unit – I

1. a) State and explain Norton’s theorem with an example. 7M b) Find the voltage drop across 12Ω resistance using Norton’s theorem for the circuit shown

in Fig.1 below:

Fig.1

8M

2. a) State and explain superposition theorem with an example. 7M b) Determine the voltage across 20Ω resistance in the circuit shown Fig.2 below, using

Superposition theorem:

Fig.2

8M

Unit – II

3. a) Describe working and principle of operation of D.C. generator. 8M b) A 4 pole, 1500 rpm D.C generator has a lap wound armature having 24 slots with 10

conductors per slot. If the flux per pole is 0.04Wb, calculate the emf generated in the armature. What would be the generated emf if the winding is wave connected?

7M

4. a) Derive an expression for Torque in a DC motor. 8M b) A four pole lap wound shunt generator delivers 200A, at terminal voltage of 250V. It has a

field and armature resistance of 50Ω and 0.05Ω respectively. Neglecting brush drop determine: i. Armature current ii. The current per armature parallel path iii. e.m.f generated iv. power developed

7M

Unit – III

5. a) What are the losses in a transformer? On what factors do they depend? And how are they minimized.

7M

b) A 25 KVA transformer has an efficiency of 94% at full load unity p.f and half full load, 0.9p.f. Determine the Iron and full load copper loss.

8M

Cont…2

::2::

6. a) Draw the equivalent circuit of a transformer. 5M b) A 200kVA transformer has an efficiency of 98% at full load. If the maximum efficiency

occurs at three quarters of full-load. Calculate the efficiency at half load. Assume negligible magnetizing current and power factor 0.8 at all loads.

10M

Unit – IV

7. a) With the help of neat sketches, explain the constructional details and working principle of three phase induction motor.

8M

b) Explain with a neat sketch, torque-slip characteristics of an induction motor.

7M

8. a) Explain the working principle of operation of capacitor start induction motor. 8M b) Explain the characteristics of stepper motor.

7M

Unit – V

9. a) Derive the EMF equation of an alternator. 7M b) A 6 pole, 3 phase, 50Hz alternator has 12 slots per pole and 4 conductors per slot. A flux

of 25mwb is sinusoidally distributed along the air gap. Determine the line e.m.f if the alternator is star connected. Given: winding factor Kd=0.96, Pitch factor Kp=1.

8M

10. a) Explain the working principle of synchronous motor. 7M b) A 6-pole, 3 phase star connected alternator has an armature with 90 slots and 8

conductors per slot, and revolves at 1000rpm, the flux per pole being 0.05 Weber’s. Calculate the emf generated if the winding factor is 0.97 and all the conductors in each phase are in series.

8M




SIGNALS AND SYSTEMS




Unit – I

1. a) Show that product of two even signals or of two odd signals is an even signal while the product of an even and odd signal is an odd signal.

7M

b) Determine the trigonometric form of Fourier series of the square wave shown in Fig.1.

Fig.1

8M

2. a) Explain the operation performed on dependent variable 7M b) A continuous time signal X (t) is shown in Fig.2. Sketch and label each of the following:

Fig.2

i. x(t-2) ii. x(2t) iii. x(t/2) iv. x(-t)

8M

Unit – II

3. a) Obtain the condition for distortion less transmission through a system. 6M b) Obtain Fourier transform of the following signals:

i. Unit impulse ii. Single sided exponential signal iii. Sinusoidal signal

9M

4. a) Derive the following properties of FT: i. Linearity ii. TimeShift iii. Frequency Shift

8M

b) Determine the Fourier transform of the rectangular pulse shown in Fig.3.

Fig.3

7M

Cont…2

:: 2 ::

Unit – III

5. a) Perform convolution of the following signals using graphical method x1(t)= e-3t u(t), x2(t)= t u(t).

7M

b) Consider an LTI discrete time system with input x(t)=e-3t [u(t)] and unit impulse response h(t)= e-t u(t). Find the output signal y(t).

8M

6. a) For the system y(t) = ex(t). Determine whether the system is: i. Linear ii. Causal iii. Stable iv. Time- invariant

8M

b) Consider a continuous time LTI system with unit impulse response h(t)=u(t+2), and input x(t)=e-2t u(t); Find the output y(t) of the system.

7M

Unit – IV

7. a) State and prove initial value theorem of Laplace transform. 5M b) State convolution theorem of Laplace transforms. Perform convolution of x1(t) and x2(t)

using convolution theorem and sketch the resultant waveform where x1(t)= u(t)-u(t-1) and x2(t)= u(t)-u(t-2).

10M

8. a) Find the Inverse Laplace transform of X(s)=(3S+4)/(S+1)(S+2)2. 8M b) Determine the Laplace transform of x(t)=eatu(t) and depict ROC and location of poles and

Zeros in the S-plane. [a is real]. 7M

Unit – V

9. a) State sampling theorem. What are the several ways of sampling continuous time signal? Explain ideal sampling.

7M

b) Find the Z-Transform of x(n)= αnu(n-1).

8M

10. a) Define initial and final value theorem of Z-Transform. 5M b) Find the Inverse Z-Transform of the sequence X(Z)=Z/(3Z2-4Z+1) for the following ROC’s.

i. 1Z

ii. 1/ 3Z

iii. 1/ 3 1Z

10M




PROBABILITY THEORY AND STOCHASTIC PROCESSES




Unit – I

1. a) Write note on uniform and exponential random variable.

7M

b) Differentiate Probability Distribution Function and Probability Density Function. List properties of density function. Write note on PDF and CDF of Gaussian Random Variable.

8M

2. a) Write note on moments of random variable. Derive expression for variance and skew. Write note on Chebyshev’s inequality.

8M

b) Determine the mean value of following exponential function:

/1

0

x a b

x

e x af x b

x a

Then from that result calculate variance and skew of the same.

7M

Unit – II

3. a) State joint density function and discuss the properties of joint density function. 7M b) Explain interval conditioning and statistical independence of multiple random variables.

8M

4. a) List the properties of multiple random variables. Discuss central limit theorem for sum of large Radom variable.

8M

b) Compute the joint characteristic function of X and Y if 1

fxy 2 exp 1 2 2

x y .2

7M

Unit – III

5. a) Define random process and state some useful classifications of random process. 6M b) Given the random process X(t)= A Sin(ωt+θ), A, ω are constants and θ is an uniformly

distributed random variable in the interval (-π, π). Define a new random process Y(t)=X2(t). Find: i. Autocorrelation function of Y(t) ii. Find the cross correlation function of X(t) and Y(t)

9M

6. a) Write a note on covariance function of random processes. 8M b) Given the random process Y t X t Cos t , where X t is a wide sense

stationary random process that amplitude modulates a carrier of constant angular

frequency . With a random phase θ independent of X t and uniformly distributed in

the interval , . Find:

i. E Y t

ii. Find the autocorrelation function of Y t

7M

Unit – IV

7. a) Discuss the relationship between power density spectrum and autocorrelation function. 8M b) Find the power spectrum of random process with the following function as

autocorrelation

2

0/ 2 cosxxR t A t

7M

Cont…2

::2::

8. a) Discuss properties of cross power density spectrum. 8M b) Discuss the relation between cross power spectrum and cross correlation function.

7M

Unit – V

9. a) Name the different types of extraterrestrial noise. Explain. 6M b) For a cascaded connection of two port networks derive the expression for overall

equivalent noise figure.

9M

10. a) For a cascaded connection of two port networks, derive the expression for overall equivalent noise temperature.

9M

b) Calculate the RMS noise voltage and thermal noise power appearing across 20Ω resistor at 250 Kelvin temperature with effective noise bandwidth of 10KHz.

6M




PRINCIPLES OF ELECTRICAL ENGINEERING (Electronics and Communication Engineering)



Unit – I

1. a) State and explain Thevenin’s theorem. Compare Thevenin equivalent with Norton’s equivalent.

6M

b) In the network shown Fig.1 below, if the load is variable both in resistance and reactance, for what value the load ZL will receive maximum power? What is the value of maximum power?

Fig.1

9M

2. a) State and prove Milliman’s theorem. 5M b) Using superposition theorem, find the current through 1Ω resistor across AB of

the network shown in Fig.2 below.

Fig.2

10M

Unit – II

3. a) A series RLC circuit with R=200Ω, L=0.1H and C=100µF has a constant voltage of 200 V applied at t=0. Find the transient current. Assume zero initial charge across capacitor.

10M

b) Explain the graphical interpretation of initial conditions of L and C elements.

5M

4. a) Show how R,L and C behaves under switching (transient) conditions , i.e at t=0+ and at t=infinity.

6M

b) In the circuit shown in Fig.3 below switch k is changed from position 1 to 2 at t=0, steady state having been reached before switching. Find i(0+), di/dt and d2i/dt2 at t=0+.

9M

Fig.3

Cont…2

:: 2 ::

Unit – III

5. a) Mention different types of generators with their circuit diagrams. 6M b) In a long-shunt compound generator, the terminal voltage is 230V, when

generator delivers 150A. Determine: i. Induced EMF ii. Total power generated Given that shunt field, series field and armature resistances are 92Ω, 0.015Ω and 0.032Ω respectively.

9M

6. a) Explain significance of the back EMF in DC motor. 6M b) A 250V dc shunt motor has shunt field resistance of 250Ω and an armature

resistance of 0.25Ω. For a given load torque and no additional resistance included in the shunt field circuit, the motor runs at 1500r.p.m drawing an armature current of 20A. If a resistance of 250Ω is inserted in series with the field, the load torque remaining the same, find out the new speed and armature current assume the magnetization curve to be linear.

9M

Unit – IV

7. a) Show and explain the appropriate equivalent circuit of a transformer. 6M b) A 25KVA single phase transformer having 500 turns on primary and 40 turns on

the secondary. The primary is connected to a 3000V, 50Hz supply. Calculate: i. Primary and secondary currents on full load ii. Secondary e.m.f iii. The maximum core flux

9M

8. a) With a neat sketch discuss how to perform the short circuit test on transformer. 6M b) A single phase 2200/250V, 50Hz transformer has a net core area of 36cm2 and a

maximum flux density of 6Wb/m2. Calculate the number of turns of primary and secondary.

9M

Unit – V

9. a) Derive the expression for maximum torque condition under running conditions in 3φ induction motor.

9M

b) A 4-pole 3φ induction motor operates from a supply whose frequency is 50Hz, calculate: i. The speed at which the magnetic field of the stator is rotating ii. The speed of rotor when the slip is 0.04 iii. The frequency of the rotor current when the slip is 0.03

6M

10. a) Draw torque-speed characteristics of 3Ф induction motor for low, medium and large rotor resistance. Explain.

6M

b) With a neat sketch, explain the working of capacitor start and run motor. 9M




DIGITAL LOGIC DESIGN

(Common to Computer Science and Engineering, Information Technology, Electronics and Communication Engineering & Electrical and Electronics Engineering)



Unit – I

1. a) Implement the following Boolean expressions using minimum number of 2 input NAND gates only: i. Y = ABCD ii. Y = A’B+AB’

7M

b) Represent the following expressions in both canonical maxterm and minterm forms in decimal notation: i. F= x’y+yz ii. F= (a’ + b) (b + c’)

8M

2. a) Perform the following: i. (11010)2 - (10000)2 Using 1’s and 2’s complement methods ii. (1000100)2 - (1010100)2 Using 1’s and 2’s complement methods

8M

b) Express the following functions by a minterm canonical form: i. F(a, b, c) = (a + b’) (a + c) ii. F(a, b, c) = a’(b’+c) + c’

7M

Unit – II

3. a) Obtain all the prime implicants and essential prime implicants for the following Boolean expression using Karnaugh map. f(a, b, c, d) = a’c’d + a’cd +b’c’d’ +ab’c +a’b’cd’.

8M

b) Find the minimal products of the following Boolean function using Karnaugh map. f(a, b, c, d)=Σm(7, 9, 11, 12, 13, 14)+ Σd(3, 5, 6, 15).

7M

4. a) Find the prime implicants and the essential prime implicants of the following Boolean function using Karnaugh map. f(a, b, c, d)=Σm(1, 3, 5, 7, 8, 10, 12, 13, 14)+ Σd(4, 6, 15).

6M

b) Obtain all the prime implicants of the following Boolean function using Quine-McCluskey method. f(a, b, c, d)=Σm(0, 2, 3, 5, 8, 10, 11).

9M

Unit – III

5. a) Design a general purpose adder/subtractor circuit that can perform one’s complement and two’s complement subtraction.

8M

b) Differentiate between synchronous and asynchronous sequential circuit.

7M

6. a) Explain the working of a JK flip-flop. What is race around condition? How can it be eliminated?

8M

b) Realize the function f(A, B, C, D)=∑m(0, 1, 5, 7, 10, 14, 15) using: i. 16:1 Multiplexer ii. 8:1 Multiplexer

7M

Unit – IV

7. a) What is the shift register? What are the four modes of operation? Explain in detail. 8M b) Implement the following functions using PLA:

F1(a,b,c) = Σ m (1,2,3,6), F2(a,b,c) = Σ m (0,1,3,6,7). 7M

Cont…2

:: 2 ::

8. a) Design MOD-8 twisted ring counter using D Flip-Flops and write the sequence of MOD-8

twisted ring counter. 7M

b) Design a ripple 4-bit UP counter. How will you convert the same counter to down counter?

8M

Unit – V

9. a) Write the excitation table and state diagram for the sequential circuit shown in Fig.1.

Fig.1

8M

b) What are synchronous sequential circuits? Explain the differences between Mealy and Moore models.

7M

10. a) What are the salient features of ASM charts? Give an example. 8M b) Write the state diagram for the given excitation table.

Present State Next State Output

Q1 Q0 X=0 X=1 X=0 X=1

Q1(t+1) Q0(t+1) Q1(t+1) Q0(t+1) y y

0 0 0 0 0 1 0 0

0 1 1 1 0 1 0 0

1 0 1 0 0 0 0 1

1 1 1 0 1 1 0 0

7M




ELECTRONIC CIRCUIT ANALYSIS




Unit - I 1. a) Derive the expression for Current gain AI and Voltage gain AV for a common emitter

configuration with unbypassed Emitter resistor. 6M

b) Calculate the Av ,AI, Zi for the circuit if hfe=100,hoe=25µA/V, hre=2.5X10-4 and hie=1.1KΩ

Fig:1

9M

2. a) Draw the circuit of CE amplifier and obtain its equivalent hybrid model and derive expressions for Ai, Ri, Av and Ro using exact and approximation analysis.

7M

b) Define h – parameters for a transistor. Why are these called hybrid parameters? What are their units?

8M

Unit – II 3. a) Draw the circuit of two Stages RC Coupled Amplifiers. Derive the expression for Overall

Voltage gain AV and input impedance Zi.

8M

b) Two RC coupled amplifiers are connected to form a 2-stage amplifier. If the lower and upper cutoff frequencies of each individual amplifier respectively are 100 HZ and 20 kHZ, What these frequencies are for the 2-stage amplifier?

7M

4. a) Derive gm, rb’e, rb’c and rce from h-parameters in Common Emitter configuration. 9M b) Define fβ and fT for CE short circuit with relevant equation. CE short circuit with

gm=50mA/V, rb’e=1KΩ, Ce=1pF and Cc=0.2pF, determine the values of fβ and fT.

6M

Unit – III

5. a) Explain the effect of negative feedback on transfer gain, input and output impedance. Illustrate with relevant expressions.

8M

b) Analyze voltage series feedback amplifiers using suitable diagrams and expressions.

7M

6. a) With the help of neat circuit diagram explain the operation of Hartley oscillator circuit 8M b) List the merits of Hartley oscillator. In Hartley oscillator L1=2mH, L2=20µH and

capacitance is variable. Find the range of C if the frequency varied from 950KHz to 2.05MHz, neglect the mutual inductance.

7M

Cont…2

:: 2 ::

Unit – IV 7. a) Explain Operation of Class A amplifier with direct coupled resistive load. Derive the

expression for output power. 8M

b) A class B amplifier provides a 20v peak output signal to 15Ω load .The system operates on a power supply of 25V. Determine the efficiency of the amplifier.

7M

8. a) What are Power amplifiers? How are they classified depending upon their mode of operation?

6M

b) Explain the following concepts with respect to large signal amplifiers: i. Crossover distortion ii. Harmonic distortion iii. Complimentary symmetry push pull class B amplifier

9M

Unit – V

9. a) Draw a small signal tuned amplifier consisting of parallel tuned circuit. Discuss the design parameters of the network.

8M

b) A single tuned RF amplifier uses a transistor with an output resistance of 50K, ouput capacitance of 15pF and input resistance of next stage is 20KΩ the tuned circuit consists of 47pF capacitance in parallel with series combination of 1µH inductance and 2Ω resistance. Calculate: i. Resonant frequency ii. Effective quality factor iii. Bandwidth

7M

10. a) With neat diagram explain single tuned capacitive coupled Amplifier. 7M b) Design a single tuned amplifier for the following specifications

centre frequency=500KHz and bandwidth=10KHz.Assume transistor parameters gm=0.04, hfe=100, Cbe=1000pf and Cbc=100pF.the bias network and input resistance so that ri=4KΩ and RL=510Ω.

8M




ELECTRONIC DEVICES AND CIRCUITS




Unit – I

1. a) Derive the expression for Volt-Ampere relation of PN diode and explain the V-I characteristics.

7M

b) For a silicon diode at working temperature of 25°C, the forward voltage applied across the diode is 0.5V. Determine its forward current if the reverse saturation current is

10A.

8M

2. a) Explain the operation of a half wave rectifier, with neat diagrams. Derive the expression for output DC voltage VDC.

8M

b) In a full wave rectifier, the transformer secondary voltage is 120V. The load resistance is 1950Ω and each of the diodes employed has a forward resistance of 50Ω. Find the load current and rms value of the input current.

7M

Unit – II

3. a) Explain the operation of a PNP transistor and draw its current components. 8M b) Explain the input and output characteristics of CE configuration of a BJT.

7M

4. a) Explain any two bias compensation techniques with neat diagrams. 7M b) In a fixed bias circuit, a Silicon transistor with β=100 is used, Vcc=6V, Rc=3kΩ,

RB=530kΩ. Draw DC load line, determine the Q point & Find Stability factor.

8M

Unit – III

5. a) Draw h parameter equivalent model for CE circuit and derive the expressions for input resistance Zi and Voltage gain Av.

8M

b) A common base transistor has the following h-parameters hib=22Ω, hrb=2.9x10-4, hfb=-0.98,hob=0.49x10-7mho. It is driven by a voltage source Vs of internal resistance Rs=1000Ω.,if the load resistance is 12KΩ, find Ai and Av.

7M

6. a) Draw the hybrid model for the CB and CC configurations. And compare them. 5M b) Consider a single stage CE amplifier with Rs=1KΩ, R1=50KΩ, R2=2KΩ, RC=1KΩ, RL=1.2KΩ,

hfe=50, hie=1.1K, hoe=25μA/V and hre=2.5X10-4. Find Ai, Ri and R0.

10M

Unit – IV

7. a) Draw the symbol, structure of a n-channel JFET and explain its parameters such as drain resistance, transconductance and amplification factor.

8M

b) List out the differences between JFET and MOSFET.

7M

8. a) Explain the construction and characteristics of n-channel enhancement mode MOSFET with neat diagrams.

8M

b) Explain the construction and characteristics of n-channel depletion mode MOSFET with neat diagrams.

7M

Unit – V

9. a) With neat diagram explain colpitts oscillator. 8M b) Illustrate the Barkhausen criterion for an oscillator.

7M

10. a) Draw Crystal oscillator and derive the expression for frequency of oscillation. 8M b) Discuss the general characteristics of negative feedback amplifiers. 7M




DC MACHINES (Electrical and Electronics Engineering)



Unit – I

1. a) Describe the principle of energy conversion. From a consideration of the various energies involved, develop the model of an electro mechanical conversion device.

8M

b) Show that the torque developed in a doubly excited magnetic system is equal to the rate of increase of field energy with respect to the displacement at constant currents.

7M

2. a) Define field energy and co-energy. Give the significance of co-energy in the derivation of torque or force in an electro mechanical energy conversion device.

8M

b) A coil of an electromagnetic relay is associated with a magnetic circuit whose reluctance is given by a+bx. Where a and b are positive constants decided by the details of the magnetic circuit in which x is length of the air gap between fixed and movable members. If the coil is connected to an AC voltage given by VmSinwt, find the expression for average force on armature, with air gap held constant at x.

7M

Unit – II

3. a) Draw the cross sectional view of a dc machine. Mention the function of each part. 8M b) Derive the expression for number of conductors/pole of the compensating winding.

7M

4. a) Derive the expression for demagnetizing ampere turns/pole and cross magnetizing ampere turns/pole.

8M

b) A 4 pole wave wound, 220 volts dc shunt generator has a full load current of 22A and shunt field current of 2A. Find demagnetizing ampere turns/pole and cross magnetizing ampere turns/pole, if the brushes are given a lead of 2 commutator segments at full load. There are 111 commutator segments and 4 turns /coil.

7M

Unit – III

5. a) A short shunt compound generator supplies a load current of 100A at 250V. The generator has the following winding resistances: Shunt field 130Ω, armature 0.1Ω and the series field 0.1Ω. Find the emf generated, if the brush drop is 1V per brush.

7M

b) Briefly explain the reasons and the necessary conditions for operating D.C. generators in parallel.

8M

6. a) Define the following terms: i. Critical field resistance ii. Critical load resistance iii. Critical speed

6M

b) In a certain substation there are 5 d.c. shunt generators in parallel, each having an armature resistance of 0.1Ω, running at the same speed and excited to give equal induced emfs. Each generator supplies an equal share of a total load of 250kW at a terminal voltage of 500V into a load of fixed resistance. If the field current of one generator is raised by 4%, the other remaining unchanged, calculate the power output of each machine and their terminal voltages under these conditions. Assume that the speeds remain constant and flux is proportional to field current.

9M

Cont…2

:: 2 ::

Unit – IV

7. a) Derive the expression for armature torque in a dc motor. 7M b) A 440V DC motor takes an armature current of 20A and runs at 500rpm. The

armature resistance is 0.6Ω. If the flux is reduced by 30% and the torque is increased by 40%, what are the new values of armature current and speed?

8M

8. a) Draw and explain Ta versus Ia and N versus Ta characteristic of a DC series motor. 8M b) A shunt motor has armature resistance of 0.1Ω. It is connected across the 220V

DC supply. The armature current taken by the motor is 20A and runs at 800rpm. Calculate the additional resistance to be inserted in series with the armature to reduce the speed to 520rpm. Assume that there is no change in armature current.

7M

Unit – V

9. a) Derive the condition for maximum efficiency for a D.C machine when it is working as a generator.

7M

b) A 5kW, 250V, 2000rpm shunt motor takes a no load line current of 3.5A and a field current of 1A at 250V, 2000rpm. Estimate the efficiency of the machine as a 5kW generator at a terminal voltage of 250V. Assume armature resistance 1Ω.

8M

10. a) List the advantages and disadvantages of Hopkinson’s test. 5M b) Two identical D.C machines when tested by Hopkinson’s method gave the

following test data: Field currents are 2.5A and 2A. Line voltage is 220V. Line current is 10A. Motor armature current is 73A. The armature resistance of each machine is 0.05Ω. Calculate the efficiency of motor. Use including field current method.

10M




ELECTRONIC DEVICES (Common to Electronics and Communication Engineering &

Electrical and Electronics Engineering) Date: 20 November, 2017 FN Time: 3 hours Max Marks: 75


Unit – I

1. a) Write in brief drift and diffusion currents in a semiconductors. 6M b) What are the major blocks of the oscilloscope, and what does each do?

9M

2. a) Show how amplitude, frequency and phase can be measured using a CRO. 9M b) Describe Hall effect, what properties of a semiconductor are determined from a Hall

effect experiment.

6M

Unit – II

3. a) Explain the working of a Zener diode and explain its V-I characteristics. 8M b) Briefly explain the two major types of diode junction capacitance.

7M

4. a) How a PN junction diode is working? Draw and explain V-I characteristics of PN diode with neat diagram.

8M

b) Explain the V-I characteristics of ideal diode versus practical diode.

7M

Unit – III

5. a) Explain the operation of centre tapped full wave rectifier without filter and derive expression for ripple factor.

8M

b) Compare three rectifier circuits namely, HWR, centre-tapped FWR and bridge Rectifier.

7M

6. a) Draw sketches to show the basic construction and equivalent circuit of a UJT. Briefly explain the device operation.

7M

b) With neat sketches explain the construction and working of tunnel diode.

8M

Unit – IV

7. a) Describe the consequences of Early effect. 5M b) With the help of transfer characteristics, explain operation of n – channel

enhancement MOSFET.

10M

8. a) Summarize the salient feature of BJT operating in CE, CB, CC configurations. What is significance of common collector configuration?

7M

b) Plot the transfer characteristics of JFET with IDSS =10mA and VP=_ 4V.

8M

Unit – V

9. a) Define biasing. What causes instability in biased circuit of BJT? Define the stability factors S, S’ and S’’.

6M

b) JFET amplifier with voltage divider bias has the following specifications: VP=-2V, IDSS=4mA, RD=910Ω, RS=3KΩ, R1=12MΩ, R2=8.57MΩ, VDD=24V . Find the operating point.

9M

10. a) Explain bias compensation techniques using thermistor and sensistor. 6M b) A Ge transistor uses potential divider method of biasing with VCC=16V, R1=56KΩ,

R2=20KΩ, RC=3KΩ and RE=2KΩ and α=0.985. Determine the operating point. 9M




ELECTRICAL MACHINES-I (Electrical and Electronics Engineering)



Unit – I

1. a) Draw a neat sketch of a d.c machine and label the parts. 7M b) A 4 pole, lap wound d.c shunt generator has a flux per pole of 0.07 webbers. The

armature winding consists of 220 turns each of 0.004 ohms resistance. Calculate the terminal voltage when running at 900 r.p.m if the armature current is 50 A.

8M

2. a) With usual notations derive the expressions for demagnetizing and cross - magnetizing ampere turns pole per

9M

b) Mention the advantages and disadvantages of using carbon brushes over copper brushes in d.c machines.

6M

Unit – II

3. a) Draw the circuit diagrams for series, shunt, long shunt and short shunt generators and also write relevant circuit equations.

8M

b) A d.c shunt generator has the following magnetization characteristics:

Field current 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Open circuit emf 54 107 152 185 210 230 245

The armature and field resistances are 0.1 ohms and 80 ohms respectively. Calculate i. The voltage to which the machine will excite when run as a shunt generator at

same speed ii. The % reduction in speed for the machine to fail to excite on open circuit

7M

4. a) Mention the conditions to be satisfied for voltage build up in shunt generator. 5M b) A short – shunt d.c compound generator supplies 200A at 100V. The resistance of

armature, series and shunt field windings is 0.04, 0.03 and 60Ω respectively. Find the emf generated. Also find the emf generated if the same machine is connected as long shunt machine.

10M

Unit – III

5. a) Describe the experimental set up for Hopkinson’s test and explain its necessity and use.

6M

b) A 10kW, 250V shunt motor has an armature resistance of 0.5Ω and a field resistance of 200Ω. At no load, and rated voltage, the speed is 1200 rpm and the armature current is 3A. At full load and rated voltage the line current is 47A and because of armature reaction, the flux is 4% less than its no load value: i. What is the full load speed ii. What is the developed torque at full load

9M

6. a) Explain Ward Leonard system of speed control with relevant diagram 7M b) A 220 volts d.c shunt motor at no load takes a current of 2.5A. The of armature and

shunt field are 0.8 ohms and 220 ohms respectively. Estimate the efficiency of motor when the input current is 20A.

8M

Cont…2

::2::

Unit – IV

7. a) How is parallel operation of transformer done? What are its advantages? Explain how it is done for transformers with equal voltage ratios?

7M

b) The efficiency of a 1000kVA, 110/220V 50hz single phase transformer is 98.5% at half fullload at 0.8pf leading and 98.8%at full load upf determine: i. Iron Loss ii. Full load copper loss iii. Maximum efficiency at upf

8M

8. a) What are the losses in a transformer? How can it be minimized? 7M b) A 400/100V, 10kVA, 2-Winding Transformer is to be employed as an auto transformer

to supply a 400V circuit from a 500V source. When tested, as a 2_winding Transformer at rated load,0.8pf lagging, its efficiency is 0.97: i. Determine its kVA rating as an auto transformer ii. Find its efficiency as an autotransformer

8M

Unit – V

9. a) Draw the circuit and phasor diagram for obtaining three phase to two phase conversion as suggested by Scott. Also write the expressions for teaser current, main currents on primary, secondary teaser current and secondary main current.

9M

b) Two transformers connected in open delta supply a 400kVA balanced load at 0.866 power factor(lag). The load voltage is 440V. What is the kVA and kW supplied by each transformer?

6M

10. a) Discuss off load and on load tap changing transformers with neat figures. 9M b) A 100kVA, 3 phase, 50Hz, 3300 / 400V, transformer is delta connected on the h.v side

and Y connected on l.v side. The resistance of the h.v winding is 3.5 ohms per phase and that of l.v winding is 0.02 ohms per phase. Calculate the iron losses of the transformer at normal voltage and frequency if it's full load efficiency is 95.8% at 0.8 power factor (lag).

6M




ELECTROMAGNETIC FIELDS

(Electrical and Electronics Engineering)



Unit – I

1.

a) Determine electric field intensity at any point due to an infinite sheet of charge having uniform surface charge density ρs. Verify the result using Gauss’s law.

8M

b) An infinite uniform line charge ρL = 2 nC/m lies along the x axis in free space, while

point charges of 8 nC each are located at (0,0,1) and (0,0,-1). Find E at (2,3,-4).

7M

2. a) Define electric field intensity and electric flux density with their units. Obtain the electric field at any point due to an infinite line charge having line charge density ρL. Verify the result using Gauss’s law.

9M

b) State Coulomb’s Law. Point charges of 50nC each are located at A(1, 0, 0), B(−1, 0, 0), C(0, 1, 0), and D(0,−1, 0) in free space. Find the total force on the charge at A.

6M

Unit – II

3. a) State and explain: i. Ampere’s circuital law ii. Biot- Savart’s Law

8M

b) Given the field H = 20ρ2 aφ A/m: i. Determine the current density J ii. Integrate J over the circular surface ρ = 1, 0 < φ < 2π, z = 0, to determine the total

current passing through that surface in the az direction

7M

4.

a) Using Biot-Savart’s law, obtain an expression for magnetic field intensity H at any point on the axis of a circular current loop.

7M

b) A current filament on the z axis carries a current of 7 mA in the az direction, and current sheets of 0.5 azA/m and −0.2 azA/m are located at ρ = 1cm and ρ = 0.5cm, respectively. Calculate H at: i. Just inside and just outside of the current sheet where ρ = 0.5cm ii. ρ = 1.5cm

8M

Unit – III

5. a) Obtain point form of continuity equation. 7M

b) Using Laplace’s equation show that the capacitance of the concentric spheres is 4

1 1

a b

where V=0 at r=b; V=V0 at r=a; b>a.

8M

6. a) Obtain the boundary condition at the interface of a conductor and dielectric. 8M b) A solenoid of 200 turns wound tightly on a cylindrical tube of length 60cm and of

diameter 6cm, given that medium is air. Find the inductance. Derive the formula used.

7M

Cont…2

::2::

Unit – IV

7.

a)

Explain the concept of scalar and vector magnetic potential.

8M

b) A point charge for which Q = 2×10−16 C and m = 5×10−26 kg is moving in the combined

fields E = 100ax − 200ay + 300az V/m and B = −3ax +2ay − az mT. If the charge velocity at t = 0 is v(0) = (2ax − 3ay − 4az) × 105 m/s. Find the unit vector showing the direction in which the charge is accelerating at t = 0.

7M

8.

a)

Explain: i. Lorentz force equation ii. Magnetic dipole moment

6M

b) Derive an expression for torque on a rectangular current loop placed in a uniform magnetic field. Find the torque vector on a square loop having corners (-2,-2, 0), (2,-2, 0), (2,2,0) and (-2,2,0) about the origin by B= 0.6ax-0.4ay T.

9M

Unit – V

9. a) Write the final set of Maxwell’s Equations for time varying fields in differential and integral form.

8M

b) A 50V voltage generator at 20MHz is connected to the plates of an air dielectric parallel plate capacitor with plate area 2.8cm2 and separation distance 0.2mm. Find the maximum value of displacement current density and displacement current.

7M

10. a) Name the two EMFs for the two cases of flux variation with respect to time. Derive an expression for both these cases starting from the Faraday’s Law of electromagnetic induction.

8M

b) In a material for which the conductivity = 5.0 S/m and εr = 2, the electric field E = 120 sin1010 t V/m. Find the conduction and displacement current densities, and the frequency at which they have equal magnitudes.

7M




NETWORK ANALYSIS

(Electrical and Electronics Engineering)



Unit – I

1. a) State and explain Superposition theorem with an example. 7M b) Using Superposition theorem, calculate the current through (2+j3) Ω impedance of the

circuit shown in Fig.1.

Fig.1

8M

2. a) State and explain Reciprocity theorem. 6M b) For the circuit shown in Fig.2 using Millman’s theorem, find the current in the load

impedance, ZL=(2+j4)Ω.

Fig.2

9M

Unit – II

3. a) Derive the equation for the voltage and current in delta connected system. 8M b) A balanced delta connected load of 2+j3Ω per phase is connected to three phase 440V

supply. The line current is 10 Amps. Find the active power, reactive power and apparent power in the circuit.

7M

4. a) A three phase balanced delta connected system of 3+j8Ω per phase is connected across 400V 3phase supply. Calculate the line currents and phase currents.

8M

b) The two wattmeter are used to measure power in a three phase load the wattmeter readings are 400W and 35W. Calculate the active power, power factor and reactive power.

7M

Unit – III

5. a) Explain the geometrical interpretation of initial conditions. 8M

b) For the circuit switch K is closed at t = 0 in Fig.3, determine i(0+), 0di

dt and

2

2

0d i

dt

Fig.3

7M

Cont…2

::2::

6. a) Derive the expression for current i(t) for the series RC circuit excited by DC voltage source.

8M

b) Refer the RL circuit shown in Fig.4. Find the complete response for i(t) for t ≥ 0+. Take i(0) = 0A.

Fig.4

7M

Unit – IV

7. a) Explain Low pass, Band pass and Band stop filters. Draw the output verses frequency response of these filters with their cut-off frequencies.

8M

b) Design a high pass constant K filter having a cut off frequency of 1KHz with a load resistance of 600Ω.

7M

8. a) Explain T-type and Bridged T-type attenuator. Write the design expressions for these attenuators in terms of attenuation factor N.

8M

b) Design a m- derived high pass filter with cut off frequency of 10KHz, design impedance of 500Ω and m=0.4.

7M

Unit – V

9. a) Draw the locus diagram for series RL circuit with fixed L and variable R. 8M b) An R-C series circuit with R=20Ω and variable capacitance is in parallel with R-L series

with R=5Ω and XL=20Ω draw the current locus for an applied voltage of 220V.

7M

10. a) Draw the locus diagram for series RL circuit with fixed R and variable L. 8M b) State the following properties of Fourier series:

i. Frequency shift ii. Linearity

7M




MATHEMATICS-III

(Common to Electronics and Communication Engineering & Electrical and Electronics Engineering)



Unit – I

1.

a) Express dxxx pnm )1(

1

0

in terms of the function and hence evaluate dxxx 1031

0

5 )1(

8M

b)

Find the value of

1 12

4 40 0

1

1 1

xdx dx

x x

7M

2. a) Prove the following: 0 2 4

i. cos( sin ) 2 cos 2 cos 4 ...x J J J 1 3

ii. sin( sin ) 2 sin sin 3 ...x J J

8M

b) Prove that 1

1

( ) ( ) 0m n

P x P x dx

for m n

7M

Unit – II

3.

a) Show that the function 2

f x z is continuous at every point but is not differentiable

at any point other than the origin.

7M

b) Find the constant such that cos3xu e y is the real part of analytic function

( )f z u iv . Also find the imaginary part of ( )f z

8M

4.

a) Find the real and imaginary parts of cot z

7M

b) Find the analytic function ( )f z u iv given (cos sin )xu v e y y

8

8M

Unit – III

5.

a)

State and prove Cauchy’s integral theorem.

8M

b) Evaluate 2

C

z dz along the straight line from 0z to 3z i

7M

6.

a) Evaluate 2( 1)( 2)

C

zdz

z z using Cauchy’s integral formula, where 12

:| 2 |C z

7M

b) Find the Laurent’s series expansion of 1

( )( 2)( 3)

zf z

z z

in the region 2 3z

8M

Cont…2

::2::

Unit – IV

7.

a) Evaluate 2 2( 4)

C

dz

z using Residue theorem, where :| | 2C z i

7M

b) Determine the poles and residues of the function 2

2( 1)( 2)

zf z

z z

8M

8.

a) Evaluate

2

0

1 2cos

5 4cosd

7M

b) Use the method of contour integration to prove that 2

0

2

cos, 0

1

mmxdx e m

x

8M

Unit – V

9.

a)

Find the image of the circle | 2 | 2z i under the transformation 1zw

7M

b)

Find the bilinear transformation that transforms the points , 0, 1 onto the points

1, 1, i respectively.

8M

10.

a) Define Planar graph, Complete graph and Bipartite graph with examples and neat diagrams.

6M

b) Using Kruskal’s algorithm, find a minimal spanning tree for the following weighted graph shown below.

9M




MECHANICS OF SOLIDS

(Mechanical Engineering)



Unit – I

1. a) Explain stress-strain diagram for mild steel with salient features. 6M b) A bar of diameter 20mm and length 100mm extends by 0.2mm. If E of the material of

the rod is 2 x 105N/mm2, what load and type of load applied to the rod. If an extension of 20% greater is required for the same load applied above, how much the diameter of bar need to be reduced.

9M

2. a) Define the following terms: i. Poisson’s ratio ii. Modulus of rigidity iii. Bulk Modulus iv. Factor of safety

6M

b) Determine the changes in length, width and thickness of a steel bar which is 4m long, 30mm wide and 20mm thick and is subjected to an axial pull of 30kN in the direction of length. E=210Gpa and µ=0.3. Also determine the volumetric strain, change in volume and final volume of the given bar.

9M

Unit – II

3. a) Establish relationship between distributed load, shear force and bending moment. 7M b) Draw SFD and BMD for a simply supported beam carrying a uniformly varying load from

zero at one end to ‘W’ per unit length at the other end.

8M

4. a) Explain different types of beams with neat sketches. 7M b) A cantilever beam 2m long is loaded with a udl of 10kN/m run over a length of 1.5m

from the free end. It also carries a point load of 10kN at a distance of 0.5m from the free end. Draw the SFD and BMD for the beam.

8M

Unit – III

5. a) State the assumptions made in the theory of simple bending. 5M b) Compare the flexural strength of the following three beams of equal weigh:

i. I section 200mm x 300mm having 10mm flange thickness of 10mm web thickness ii. A rectangular section having depth equal to twice the width iii. Solid circular c/s

10M

6.

a) Prove that with usual notation M E

I Y R

.

7M

b) A T-shaped flange shown in Fig.1 is subjected to vertical shear force of 100kN. Calculate the shear stress at neutral axis, junction and flange. MI about horizontal neutral axis is 0.0001134m4.

Fig.1

8M

Cont…2

::2::

Unit – IV

7. a) State Maculay method and derive deflection equation by using this method. 8M b) A cantilever beam subjected to forces as shown in Fig.2. Determine the slope at

B and C. Take E=200kN/m2 I=40x106mm4:

Fig.2

7M

8. a) Derive deflection of cantilever beam with UDL. 5M b) Find slope and deflection of free and of the cantilever beam E=200kN/m2 I=40x106mm4,

as shown in Fig.3.

Fig.3

10M

Unit – V

9. a) Derive an expression for circumferential stress for thin cylinder. 6M b) A thick spherical shell of 160mm internal diameter is subjected to an internal pressure of

40N/mm2. Find the thickness of shell if the permissible tensile stress is 80N/mm2.

9M

10. a) Derive an expression for longitudinal stress for thin cylinder. 6M b) Find the thickness of metal necessary for a cylindrical shell of internal diameter 160mm

to withstand an internal fluid pressure of 8N/mm2. The maximum allowable or permissible or hoop’s stress in the section is not exceeding 35N/mm2.

9M




MECHANICS OF FLUIDS (Mechanical Engineering)



Unit – I

1. a) Define surface tension. Prove that the relationship between surface tension and pressure inside a droplet of liquid in excess of outside pressure is given by p=4ς/d.

6M

b) The space between two square flat parallel plates is filled with oil. Each side of the plate is 60cm. The thickness of the oil film is 12.5mm. The upper plate, which moves at 2.5m/s requires a force of 98.1N to maintain the speed. Determine: i. The dynamic viscosity of the oil in poise ii. The kinematic viscosity of the oil in stokes if the specific gravity of the oil is 0.95

9M

2. a) What is a manometer? How are they classified? 6M b) A differential manometer is connected between the two pipes A and B. Pipe A is 3cm

above the pipe B. The mercury level in the manometer limb connected to the pipe A is 5m below the centre of the pipe A and is at a higher level than that at in the limb connected to pipe B. The pipe A carries a liquid of specific gravity 1.5 and is maintained at a pressure of 10N/cm2, while the pipe B carries a liquid of specific gravity 0.9 and maintained at 18N/cm2. Find the difference in mercury level in the differential manometer.

9M

Unit – II

3. a) Distinguish between: i. Steady flow and unsteady flow ii. Uniform and non uniform flow iii. Compressible and incompressible flow iv. Rotational and irrotational flow v. Laminar and turbulent flow

10M

b) A 30cm diameter pipe, conveying water, branches into two pipes of diameters 20cm and 15cm respectively. If the average velocity in the 30cm diameter pipe is 2.5m/sec, find the discharge in this pipe. Also determine the velocity in 15cm pipe if the average velocity in 20cm diameter pipe is 2m/sec.

5M

4. a) Explain the following terms: i. Path line ii. Streak line iii. Stream line iv. Stream tube

8M

b) A 25cm diameter pipe carries oil of specific gravity 0.9 at a velocity of 3m/s. At another section the diameter is 20cm. Find the velocity at this section and also mass flow rate of oil.

7M

Unit – III

5. a) Derive an expression for the loss of head due to sudden enlargement. 7M b) Find the loss of head when a pipe diameter of 200mm is suddenly enlarged to a

diameter of 400mm. The rate of flow of water through the pipe is 250litres/sec. 8M

Cont…2

:: 2 ::

6. a) How will you determine the loss of head due to friction in pipes by using Darcy’s formula?

6M

b) A venturimeter is used for measurement of discharge of water in a horizontal pipeline. If the ratio of upstream pipe diameter to that of throat is 2:1, upstream diameter is 300mm, the difference of pressure between the throat and upstream is equal to 3m head of water and loss of head through meter is one eighth of the throat velocity head, calculate discharge in the pipe.

9M

Unit – IV

7. a) Define: laminar boundary layer, turbulent layer, laminar sub-layer and boundary layer thickness.

8M

b) For the velocity profile given as u/U=2(Y/δ)-(Y/δ)2, find the thickness of boundary layer at the end of the plate and the drag force on one side of a plate 1m long and 0.8m wide when placed in water flowing with a velocity of 150mm per second. Calculate the value of co-efficient of drag also. Take µ for water= 0.01 poise.

7M

8. a) What do you mean by separation of boundary layer? What is the effect of pressure gradient on boundary layer separation?

6M

b) The radial clearance between a hydraulic plunger and the cylindrical walls is 0.1mm: the length of the plunger is 300mm and diameter 100mm. Find the velocity of leakage and rate of leakage past the plunger at an instant when the difference of the pressure between the two ends of the plunger is 9m of water. Take µ= 0.0127poise.

9M

Unit – V

9. a) Obtain an expression for velocity of the sound wave in a compressible fluid in terms of change of pressure and change of density.

8M

b) An aeroplane is flying at a height of 15km where the temperature is -500C. The speed of the plane is corresponding to M=2. Assuming k=1.4 and R=287J/kgK, find the speed of the plane.

7M

10. a) Define the following terms: i. Sub-sonic flow ii. Supersonic flow iii. Sonic flow iv. Mach angle v. Mach cone

10M

b) Find the velocity of bullet fired in standard air if the Mach angle is 300. Take R=287J/kgK and k=1.4 for air. Assume temperature as 150C.

5M




METALLURGY AND MATERIAL SCIENCE (Mechanical Engineering)



Unit – I

1. a) Define a unit cell. Calculate the atomic radius and packing factor for BCC crystal structure. 8M b) Explain the effect of grain boundaries on the properties of material.

7M

2. a) What do you mean by crystal imperfections? Explain briefly point imperfection and surface imperfection.

9M

b) What is a solid solution? Explain Hume-Rothery’s rule.

6M

Unit – II

3. a) Explain the lever rule with example. 7M b) Construct a phase diagram using the following data and label all the fields:

Melting point of Ag=9610C Eutectic temperature=7800C Solubility of Cu in Ag=9% at 7800C Solubility of Ag in Cu=9% at 7800C Melting point of Cu=10800C Eutectic composition=28% Cu balance Ag Solubility Cu in Ag=2% at 00C Solubility Ag in Cu=4% at 00C Determine the following: i. Solidification start and end of temperature for 30% Ag alloy ii. Temperature at which a 15% Cu alloy has 50% liquid phase and 50% solid phase iii. Percentage composition of liquid and solid phase in 20% Ag alloy at 9000C

8M

4. a) With help of equilibrium diagram, explain the cooling of steel containing 0.83% C. 7M b) With a neat figure explain two component or Binary phase diagram, completely soluble in

both liquid and solid state.

8M

Unit – III

5. a) Give the composition, microstructure and applications of: i. Malleable cast iron ii. Mild steel

8M

b) Differentiate between normalizing and annealing with neat sketches.

7M

6. a) What is hardenability? Explain with neat sketch Jominy-end quench test. 7M b) Draw the TTT diagram for plain carbon eutectoid steel and explain the critical cooling

rate. 8M

Unit – IV

7. a) Write a short note on: i. Cupro Nickel ii. Bronze

7M

b) Explain about ceramic refractory material. 8M 8. a) Write brief note on alpha plus beta brasses with microstructure. 7M b) Explain the properties and applications of glass ceramics. 8M

Cont…2

:: 2 ::

Unit – V

9. a) What is a composite material? Explain briefly the role of each ingredient in a composite material.

7M

b) With a neat sketch explain hand lay up process of making composite materials. 8M 10. a) What is metal matrix composite material? Explain briefly. 8M b) What is FRP? Explain in details. 7M




MATHEMATICS FOR AEROSPACE ENGINEERS

(Aeronautical Engineering)



Unit – I

1.

a) Express dxxx pnm )1(

1

0

in terms of the function and hence evaluate dxxx 1031

0

5 )1(

8M

b)

Find the value of

1 12

4 40 0

1

1 1

xdx dx

x x

7M

2. a) Prove the following: 0 2 4

i. cos( sin ) 2 cos 2 cos 4 ...x J J J 1 3

ii. sin( sin ) 2 sin sin 3 ...x J J

8M

b) Prove that 1

1

( ) ( ) 0m n

P x P x dx

for m n

7M

Unit – II

3.

a) Show that the function 2

f x z is continuous at every point but is not differentiable

at any point other than the origin.

7M

b) Find the constant such that cos3xu e y is the real part of analytic function

( )f z u iv . Also find the imaginary part of ( )f z

8M

4.

a) Find the real and imaginary parts of cot z

7M

b) Find the analytic function ( )f z u iv given (cos sin )xu v e y y

8

8M

Unit – III

5.

a)

State and prove Cauchy’s integral theorem.

8M

b) Evaluate 2

C

z dz along the straight line from 0z to 3z i

7M

6.

a) Evaluate 2( 1)( 2)

C

zdz

z z using Cauchy’s integral formula, where 12

:| 2 |C z

7M

b) Find the Laurent’s series expansion of 1

( )( 2)( 3)

zf z

z z

in the region 2 3z

8M

Cont…2

::2::

Unit – IV

7.

a) Evaluate 2 2( 4)

C

dz

z using Residue theorem, where :| | 2C z i

7M

b) Determine the poles and residues of the function 2

2( 1)( 2)

zf z

z z

8M

8.

a) Evaluate

2

0

1 2cos

5 4cosd

7M

b) Use the method of contour integration to prove that 2

0

2

cos, 0

1

mmxdx e m

x

8M

Unit – V

9.

a)

Find the image of the circle | 2 | 2z i under the transformation 1zw

7M

b)

Find the bilinear transformation that transforms the points , 0, 1 onto the points

1, 1, i respectively.

8M

10.

a) Find the image of the circles 1z and 2z under the mapping 1

w zz

7M

b) Find the bilinear transformation which has 1 and -1 as fixed points and which maps

12

to 0

8M




FLUID MECHANICS (Civil Engineering)



Unit – I

1. a) Explain the following terms related to fluid: i. Specific weight ii. Viscosity iii. Vapour pressure iv. Capillarity v. Surface tension

10M

b) Find the surface tension in a soap bubble of 40 mm diameter when the inside pressure is 2.5 N/m2 above atmospheric pressure.

5M

2. a) Derive an expression for the depth of centre of pressure from free surface of liquid of an inclined plane surface sub-merged in the liquid.

9M

b) Determine the total pressure and centre of pressure on an isosceles triangular plate of base 4 m and altitude 4 m when it is immersed vertically in an oil of specific gravity 0.9. The base of the plate coincides with the free surface of oil.

6M

Unit – II 3. a) Obtain the equation of continuity for a three dimensional flow. 8M b) Distinguish between:

i. Path line and stream line ii. Rotational flow and irrotational flow

7M

4. a) A 200mm diameter pipe conveying water branches into two pipes of diameters 150mm and 100mmrespectively. If the average velocities in the 200mm diameter pipe and the 150mm diameter pipe are respectively 3m/sec and 1.8m/sec, determine the velocity in the 100mmpipe.

8M

b) If a potential function is given by Ø=3(x2+y2), calculate the velocity components at the point (2, 3).

7M

Unit – III

5. a) Write short notes on displacement thickness, momentum thickness and energy thickness. 8M b) Explain the concept of boundary layer. Mention the various laws assumed for velocity

distribution in laminar boundary layer.

7M

6. a) Derive an expression for Drag and Lift of submerged bodies in the liquid. 10M b) What are the conditions changing laminar flow to turbulent flow?

5M

Unit – IV

7. a) Explain the principle of venturimeter with a neat sketch. Derive the expression for the rate of flow of fluid through it.

10M

b) An orifice meter with orifice diameter 10cm is inserted in a pipe of 20cm diameter. The pressure gauges fitted upstream and downstream of the orifice meter give readings of 19.62N/cm2 and 9.81N/cm2. Find the discharge of water through pipe. Take Cd=0.6.

5M

Cont…2

:: 2 ::

8. a) Derive an expression for discharge through an orifice meter. 9M b) A horizontal venturimeter with inlet and throat diameters 30cm and 15cm respectively is

used to measure the flow of water. The reading of differential manometer connected to the inlet and throat is 20cm of mercury. Determine the rate of flow. Take coefficient of discharge = 0.98.

6M

Unit – V

9. a) Derive Darcy Weisbach formula for the loss of head due to friction in a pipe line. 8M b) Differentiate between:

i. Viscous flow and turbulent flow ii. Hydraulic gradient line and total energy line

7M

10. a) Define equivalent pipe, when pipes are connected in parallel and when in series. 7M b) Two reservoirs, the difference of water levels of which is 15m are connected by two

parallel pipes of diameter 75mm and 150mm and length 100m each. Find the discharge in each pipe. Take f=0.0075 for all pipes. Ignore minor losses.

8M




STRENGTH OF MATERIALS-I (Civil Engineering)



Unit – I

1. a) Define the following: i. Volumetric strain ii. Bulk modulus iii. Poisson’s ratio iv. Factor of safety

5M

b) A mild steel test piece was tested in tension and the following readings were obtained. Diameter of Specimen=20mm. Length of Specimen=200mm. Extension under 30kN load=0.21mm, Yield point load =40kN, Ultimate tensile load =50kN and Length of specimen after fracture=250mm, calculate the values of: i. Young’s modulus ii. Yield point stress iii. Ultimate strength iv. Percentage elongation v. Percentage reduction in area, if the diameter of specimen at the failure is 17.5mm

10M

2. a) Derive an expression for volumetric strain due to three mutually perpendicular stresses. 7M b) Calculate the modulus of rigidity and bulk modulus of a cylindrical bar of diameter

25mm and length 1.6m, if the longitudinal strain in the bar during tensile test is four times the lateral strain. Also find the change in volume, when the bar subjected to a hydrostatic pressure of 100N/mm2. E=1x105 N/mm2.

8M

Unit – II

3. a) What are the different types of loads acting on a beam? Differentiate between a point load and a uniformly distributed load.

5M

b) A cantilever beam of length 2m carries the point loads as shown in Fig.1. Draw the shear force diagram and bending moment diagram for the cantilever beam.

Fig.1

10M

4. a) What are the sign conventions for shear force and bending moment in general? 5M b) Draw the shear force and bending moment diagrams for the overhanging beam carrying

an udl of 2kN/m over the entire length as shown in Fig.2. Also locate the point of contra flexure.

Fig.2

10M

Cont…2

:: 2 ::

Unit – III

5. a) Derive the expression for circumferential stress and longitudinal stress. 7M b) A Cylinder of Inner diameter of 3.0m and Thickness of 6.0cm contain gas. If tensile stress

in material not exceed 80 N/ mm2. Determine the Internal pressure of gas.

8M

6. a) Derive the expression for volumetric strain in Thin cylinder. 8M b) Find the thickness of metal necessary for a cylindrical shell of inner diameter 180 mm to

with stand an internal pressure of 8.0N/mm2. The maximum hoop stress in section is not exceeding 35 N/mm2.

7M

Unit – IV

7. a) Mention the assumptions made in the theory of simple bending. 5M b) A timber beam of rectangular section is to support a load of 20kN uniformly distributed

over a span of 3.6m when the beam is simply supported. If the depth of section is to be twice the breadth and stress in the timber is not to exceed 7N/mm2, find the dimensions of cross sections.

10M

8. a) Prove that the shear stress distribution in a rectangular section of a beam which is

subjected to a shear force F is given by 𝜏 =𝐹

2𝐼 𝑑2

4− 𝑦2 .

6M

b) A simply supported wooden beam of span 1.3m having a cross section of 150mm wide by 250mm deep carries a point load W at the centre. The permissible stresses are 7N/mm2 in bending and 1N/mm2 in shearing. Calculate the safe load W.

9M

Unit – V

9. a) Prove that the relation M=EId2y/dx2 where M is bending moment and E is young’s modulus and I is moment of inertia.

6M

b) A beam of length 8m is simply supported at its ends. It carries an udl of 40kN/m as shown in Fig.3. Determine the deflection of beams at its midpoint an also the position of maximum deflection if E=2x105N/mm2 and I=4.3x108mm4. Use Macaulay’s method.

Fig.3

9M

10. a) Calculate the Deflection of simply supported beam, carries point load of W KN at mid span.

7M

b) A Beam of rectangular section of 230mm width and 450mm depth is simply supported at ends. It carries Uniform Distribution Load of 10.0KN/m over span of 6.0m. Find the slope and deflection of beam. Take E=2x105N/mm2.

8M




MANAGERIAL ECONOMICS AND FINANCIAL ANALYSIS

(Common to Computer Science and Engineering, Information Technology, Electrical and Electronics Engineering & Civil Engineering)



Unit – I

1. a) Explain any four applications of Managerial economics in business decision making. 8M b) Explain different types of demand.

7M

2. a) Briefly explain measures of elasticity of demand. 8M b) “Various factors determine the level of demand for Small cars in Indian Market.” Explain.

7M

Unit – II

3. a) Explain different types of cost classifications. 7M b) What are Isoquant and Isocost curves? Explain the characteristics of Isoquant.

8M

4. a) Explain briefly internal economies of scale and external economies of scale. 8M b) Confrigity.co manufacture electronic components, the fixed cost incurred is Rs.2,00,000,

direct material cost per unit Rs.70, direct labor cost Rs.30 per unit. The selling price per unit is Rs.300. The company produced and sold 2000 units is a year. Calculate the company’s Breakeven point and margin of safety.

7M

Unit – III

5. a) Explain the features of monopolistic competition. 8M b) Explain the features of monopoly market.

7M

6. a) Explain the following: i. Two- Part pricing ii. Block pricing iii. Going rate pricing iv. Peak load pricing

8M

b) Explain price output determination under monopoly.

7M

Unit – IV

7. ABC company is planning to purchase a new machine whose cash flows are given below

Year Cash flow

Mach-A Mach-B

0 (4,00,000) (4,00,000)

1 80,000 70,000

2 1,20,000 1,40,000

3 1,30,000 1,50,000

4 80,000 65,000

5 1,60,000 1,75,000

Calculate NPV and PI at a discount rate of 10% to select the right machine.

15M

8. a) What do you understand by joint stock company? What are the advantages of joint stock company?

9M

b) What are the advantages and disadvantages of Sole proprietorship? 6M

Cont…2

:: 2 ::

Unit – V

9. From the following Trial balance of Ravi enterprises, prepare the final accounts for the year ended 31st March, 2010 and the balance sheet as on that date:

Particulars Debit (Rs) Credit (Rs)

Land and building 50,000

Purchases 1,10,000

Stock 40,000

Returns 1,500 2,500

Wages 10,000

Salaries 9,000

Office expenses 2,400

Carriage inwards 1,200

Carriage outwards 2,000

Discounts 750 1,200

Bad debts 1,200

Sales 2,05,000

Capital 1,30,000

Insurance 1,500

Commission 1,500

Plant and machinery 50,000

Furniture and fixtures 22,000

Bills receivable 20,000

Sundry debtors 40,000

Sundry creditors 25,000

Cash in hand 1,500

Cash at bank 4,500

Bills payable 2,350

Total 3,67,550 3,67,550

Adjustments: i. Closing stock amounted to Rs.60, 000 ii. Outstanding wages Rs.2,000 iii. Depreciation: Land and buildings at 5%, Plant and machinery at 10% and Furniture and

Fixtures at 10% iv. Provide further bad debts reserve at 5% on Sundry debtors v. Insurance prepaid Rs.200

15M

10. a) Define Ratio Analysis. Explain the importance of Ratio Analysis. 7M b) The following is the balance sheet of M/S ABC enterprises.

Liabilities Amount Assets Amount

Capital 5,00,000 Land and Buildings 4,00,000

Bank Loan 2,00,000 Plant & Machinery 3,00,000

Creditors 1,00,000 Furniture 1,00,000

Bill Payable 50,000 Stock 50,000

Outstanding expenses

50,000 Debtors 25,000

Cash 25,000

9,00,000 9,00,000

Sales for the year: Cash sales Rs.4,00,000 Credit sales Rs.2,00,000. Calculate: i. Current ratio ii. Liquid ratio iii. Debt equity ratio iv. Total assets to total liabilities ratio

8M

discrete mathematical structures - vardhaman · :: 2 :: 8. a) explain the structures and operations...

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