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Third Semester B.E. Degree Examination, June/July 2013

Engineering Mathematics - lll

Note: Answer FIVE full questions, selectingt leasl TWO questions from each part.

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PART - A[ *- il 0<x<nI a. Obtain the Fourier series expansion of ftxt= I ', and hence deduce[2n-x. if tr<x<2n

.r.illthat-=.* ,* , *......... (07 lvlarks)

b. Find rhe hallrange Fourier sine series of l(*) = { '' if 0 <x <fl . (06 Marks)'

In- * 1I f <x<rc'

Time: 3 hrs.

constant.

4 a. Using method of least

c. Obtain the constant term and coefficients of first cosine and sine terms in the expansion of yfrom the followins table (07 Marks)

a. Find the Fourier transform of rt*l = {" - x'' 1x <a and hence deduce l'in*-ltot*a*=1.t o. lxl>a j x' 4

b. Find the Fourier cosine and sine transform of f1x.; : xe-u*, where a > 0.

c. Find the inverse Fourier transform of e-" .

3 a. Obtain the various possible solutions of one dimensional hept equation ut - c2 u** by themethod o I separat ion ol variables. (07 Marks)

b. A tightly stretched string of length .t with fixed ends is initially in equilibrium position. It is

set to vibrate by giving each point a velocity V" rrf +l Find the disptacemenr u(x. t).' \.( i'. ..- (06 Marks)

c. Solve u** * uyy = 0 given u(x, 0) : 0, u(x, 1) : 0, u(1, y)=0andu(0, y): uo, Whereu0isa

oI least souare. Ilt ax 1 2 3 4 5

v 0.5 2 4.5 8 12.5

fit a curve y - axb for the lollowing data.

lx I I l2l3 l4l s I . .'

ly lo.s Jz l+.i I s I rz.s | .,.,,,,n

b. Solve the following LPP graphicallyt ,,' . ,/Minimize Z=20x+l6y r;lvrfllrllllzc L=Zvx+toY ,i 1 fSubject to 3x+y>6, x+y>4, x+3y>6 andx,y> 0. .r.i\ 106 Marks)

c. Use simplex method to '0-- .--' ,

Maximize Z - x - t I .5 )y l.'1 ..

Subject to the constraints x+ 2y < 160, 3x + 2y <240 and x, y ) 0.

x 0 600 120' 180' 2400 100 3 600

v 7.9 7.2 3.6 0.5 0.9 6.8 7.9

1 of 2

(07 Marks)

5a.

b.

-- c.

1OMAT31

PART - BUsing Newton-Raphson method find a real root of x + logrox :3.375 neat 2.9, corrected to

3-decimal places. (07 Marks)

Solve the following system ofequations by relaxation method:

12x+y +z=31, 2x+8y-z=24, 3x+4y+l0z=58 (07 Marks)

Find the largest eigen value and corresponding eigen vector of following matrix A by power

method

and tenth terms ofthe series.

x J 4 5 6 7 8 9

v 4.8 8,4 14.5 23.6 36.2' 52.8 73.9b. Construct an interpolating polynomial for the

difference formula.data given below using *"*"r;r*:l_",1

7 a. Solve the wave equation u11 :u(x, 0) : x(4 - x) by taking I =

b. Solve numerically the equation

4u** subject to u(0, t) = 0; u(4, t) : 0; u(x, 0) : 0;1, k : 0.5 upto four steps. (0? Marks)

^ a2(m oD

= = -

subject to the conditions u(0, 0 : 0 : u(1, 0, t > 0A Ax'

7-ordinates and hence find log.2. (06 Marks)

(07 Marks)

(07 Marks)

(06 Marks)

c. Evaluare f--I- a* bv weddle'sjl+x'

and u(x, 0): sin nx,'O < x < 1. Carryout computations for two levels taking h : / and

(07 Marks)

for the following square mesh with boundary values(06 Marks)

Fig.Q7(c)

...

8a.b.

c.

Find the z-transform of: i) sinhn0; ii) coshn0.

obtain the inverse z-transfbr- or --14 .(22-1)(42-t)

Solve the following difference equation using z-transforms:

!n+z*2yn+t + yn=n with yo:yr:0

2 of2

x 2 4 5 6 I 10

(x) 10 96 196 350 868 1746

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Time: 3 hrs.

Third Semester B.E. Degree Examination, June/July 2013Analog Electronic Gircuits

Max. Marks: 100Notez Answer FIVE full questions, selecting

at least TlltO questions from each part.

PART - AI a. What do you understand by reverse recovery time? Explain it, which is applicable to diodecircuit. (05 Marks)

b. Explain the working of centre tapped full wave rectifier circuit using diodes. Compare itwith bridge rectifier. (08 Marks)

c. Compare clipping and clamping circuitd. Explain negative clamper using equivalent circuit.Obtain the output voltage equations at dillerent leveli. (07 Marks)

2 a. Explain the load line analysis ofthe fixed bias circuit with effect of variation Is, R6 and Vg6on Q point. (06 Marks)

b. Write a short note on PNP transistor biasing. (04 Marks)c. Derive an expression for the stability factor s(lco)for a voltage divider bias circuit.

(06 Marks)d. For the transistor invefier as shown in below Fig.e.2(d). Determine the values of R6 and Rs.Take Iq(s6e : 1 1.9 mA and 0a" = 200:

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(04 Marks)

DV. Vcesqf = o,l v

,r+l T Vsq = e'l v, rL1-J- ---+ t

3a.

b.

c.

Draw_ the emitter-follower circuit. Derive expressions for i) Z1; ii) Z"; iii) A, using r"model. (08 Marks)Defure h-parameters. Draw the hybrid equivalent circuit of common-emitter configuration.

..For the emitter-follower network of Fig.e.3(c). Using r" model.iii) Z"; iv) Au. Take B = 120 and 16 : 40 KO.

+-hx

Ct!r; o=-*-1F' Tl roaf

-d

q\, ccD t>y

5 ,a.

b,'

4a.b.

c.

6a.

b.

c.

c.

8a.

b.c.

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Obtain expression for miller effect input capacitance and miller effect output capacitance.(10 Marks)

Explain high frequency response ofBJT amplifier using ac equivalent model and obtain theequation of input and output capacitances. (10 Marks)

PART-BExplain the cascade connection of general amplifier with the help of block diagram. write itsadvantages. (05 Marks)

Give the list of feedback amplifier topologies. Explain each type feed back amplifier using

bloqk diagrams. (10 Marks)

Exi-lain practical feedback circuit using FET amplifier with voltage-series feedback.(05 Marks)

Give the lislilf power amplifiers. Explain series fed class A power amplifier with necessary

circuit and oritliut waveforms. (07 Marks)

Explain the working of class-B push,pull amplifier. Derive an expression for maximumconversion efficieney. (08 Marks)

For distortion readings of Dz : 0.15, D3 = 0.0i and D4 - 0.05 with Ir : 3.3 Amps and

Rc = 4f). Determine: i) Total harmonic distortion D; ii.1 Fundamental power component;iii 1 Total power. (05 Marks)

Explain with the help of a circuit diagiam of Hartley oscillator. (06 Marks)

With the help of Barkhausen criteriorl explain the working of a BJT crystal oscillator and

write the application ofcrystal oscillator (series resonant mode). (08 Marks)

In a transistor Colpitts oscillator Cr = 1nF and Cz = 100nF. Find the value of L for a

frequency of 100 kHz. (06 Marks)

Explain JFET common source amplifier using fixed bias configuration. Obtain Zt Zo and

7a.b.

A,.Define Tran conductance gm. Derive expression for gm.

Write the advantages and disadvantages between FET and BJT.

(10 Marks)(05 Marks)(05 Marks)

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USN 06cs33

(08 Marks)

(08 Marks)(04 Marks)

(05 Marks)

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Third Semester B.E. Degree Examination, June/July 2013Logic Design

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Time: 3 hrs..':..

Max. Marks:1O0

Notez Answer FIYE full questions, selectingatleast TWO questions lfrom each part.

PART_A

I a. Why NAND and NOR gates are universal gates? Simptifo the following Booleanexpression using k - map and implement the same usingi) NAND gates only (SOP form)ii) NOR gates only IPOS form )

. F(A, B C,D) - >* (0;1, 2,4, s,12,14) + dc(8, 10). (r0 Marks)b. Find the prime implicants and essential prime implicants for the following Boolean

expression using Quine McClusky's method.F(A,B,C,D):r',,(1,3,6,7,9,10, 12, 13, 14, 15). (l0Marks)

a. Realize the Boolean expression l.

F(A, B, C, D): t'. = (2.3.4,5, 13. 15) + dc(8, 9, 10, 11) using 8 : I multiplexers andexternal gates.

b. Generate the Boolean expression for

...

a. Design a 2 -bit carry look ahead adder and explain, with an eprnple. (10 Marks)b. Draw the block diagram of4 - bit adder/ subtractor circuit using full adder and explain the

Yo : A' B', yr : ABC, yz = dg, y: :49' C using PROM.c. Write the HDL code for full adder.

same.c. Compute the sum in each of the following :

i) 7s+38ii) 8r6 + Fr6.

a. What is a fliplfop? Explain the different types of flipflopsdiagram, and excitation table.

b. Convert the SR flipflop into JK and D flipflops.c. Write a note on edge trigged flipflps.

along with truth table, circuit(10 Marks)(06 Marks)(04 Mrrks)

PART _ B

5 a. What is a register? Explain the tlpes of register along with their applications.b. Design a synckonous mod- 5 counter using JK flipflop.c. What are presettable counters? Explain with an example.

(10 Marks)(05 Marks)(05 Marks)

1of 2

r1 I06cs33

6 a. Differentiate Mealy and Moore models. (05 Marks)b. Design an aslmchronous sequential logic circuit for the following state transition diagram.

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-X:d,!--..'r,\ I

^ i-".+"

$f-_ ff{' =$do1ta,tt -..*}

'4^-r1g. Qo(b)-&" \*r

c. Draw the'sffi,trarsition diagram by row elimination method foy!*toilowinS :dr:1 - r' ,,i

'd .t.

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dS Fig' Q6&[ -=." (roMarks)

a. Draw and exptqirFtd4-Uit binary ladder D/A converter. C.,: (t0 Marks)b. Discuss any twQ)Gthods of A,/D conversim. 'q{" (r0 Marks)*se *'i;-.a. Defure(lflTl parameters ii) Open - collector gate. -, t (05 Marks)b. WhA{W CMOS characteristics? Explain. l, } (05 Marks)

". ffih" aid of a circuit diagram, explain the operation of a 2 - input Ttl, $.gND gate with

_*.p*op"n -.ollector method. ' "5,f0 urarr<gr{* ""f I

***rr* -t'lt.

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USN 06CS/IS34

(08 Marks)

(06 Marks1

Time:3

Third Semester B.E. Degree Examination, June/July 2013Discrete Mathematical Structures

hrs. Ma.x. Marks: r ooNote: Answer FIVE full questions, selecting

atleast TWO questions from each part.

PART-A

Define the symmetric difference of any two sets. Determine the sets A and B, given thatA-B= {r,3,7,tl!,B-A:{2,6,8}andAnB:{4,9}. [04marrc;IfSandTbetwosubsetsof(-J,provethatSUT:SATif.andonlyifSandTaredisjoint.

,,: (06 Marks)If Aand B are any two.sets, prove that anS-=AuB,, (04 Marks)75 children went to an amusement park where they could ride the merry - go - round, rollercoaster and Ferri's wheel. It is known that 20 of them have taken all the 3 rides and 55 ofthem have taken atleast 2 ofthe 3 rides. Each ride cost Rs. 0.50 and the total receipt of theamusement park is Rs. 70. Determine the number ol children who did not try any of thethree rides. (06 Marks)

.,..

Define a tautology and contradiction. For the propositions verify that[(p n q) -+r) <+ [-r (p n q) v r] i:i a tautology using:the truth table. (06 Marks)

c.

d.

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p-+qr rvs i,.f

."-lq -+ s !',r! ,-, .. 'r,,lj :,:: (06 Marks)

.

3 a. Write down the lollowing propositions in symbolic lorm and I3 a. Write down the lollowing propositions in symbolic lorm and find its negationi) If all triangles are right angled, then no triangle is equiangularii) For all integers n, ifn is not divisible by 2, then n is odd. (08 Marks)b. Prove that the following argument is valid,

Vx[ptxt -+ q1x1]

VxtqG) -+r(x)l.'.Vx[p(x) + r(x)]Where p(x), q(x) and r(x) are open statements that are defined for a given universe.

Prove that, for any three propositions p, q, ri) [(p " q) -+ r] <> t(p] 0 a (q -+ r)lii) [p -+ (q n r)] <+ [(p'-+ q) n (p -+ r)].

c. Using the contradiction validate the fo

c. If m is an odd integer, prove m + 1l is an even integerusing:i) Direct methodii) Indirect methodiii) Contradiction merhod.

I of 2(06 Marks)

06cs/rs34

4 a. Prove by mathematical inductionthat 12+32+52---+(2n-1)2:n(2n-1)(2n+l)

b. If Ar, Az, A: - - - A, are any sets, using mathematical induction provet,,1.lUe,l=nA, lorn>2.[,= r ) i=t

c. Find an explicit formula for

'1 ,, i) a,= an-r + n, ar: 4 for n>2ii) an=an-t 1-3, ar:10 for n>2.

:. PART-B

(06 Marks)

5 a.' Define Cartesian product of two sets. For any non empty sets A, B,'C prove that

A i(B O C) : (A x B) n (A x C). -(07 Marks)

b. Let iand g be functions domRto R defied by (x): ax+ b and g(x) = I - x + x2. If (g o f)(x) = 9xi--_9x + 3, determine a, b. (06 Marks)

c. Define innildible function. If f : A+ B andg: B -+ Care inveitible functions, then, prove

that (g o g : X.1i.,C ls invertible and (g o f)-t = f' o g-r. (07 Marks)

6 a. Define a poset (irartially ordered sdt). The directed graph for a relation R on a set

A - la. b. c. d I is shown below :

i) Verifr that (A, R) is a poset

ii) Draw the Hasse diagram i-.,.-iii) Topologically sort the poset (A, R). (07 Marks)

b. Defme an equivalence relation on a set. Prove that every partition of a set A induces an

(G. +) is an abelian group. (07 Marks)

b.'..If H and K are subgroups ofa group G prove that H 0 K is also a sub group ofG. (06 Marks)

,, c. State and prove Lagrange's theorem. (07 Marks)

....-.:! a. Define a ring. Prove that the set Z with binary operations @ and @ defined by

...i,'' x O y: x + y- l, x I y: x + y- xy is a ring. (08 Marlis)

b. The encoding function E :222 -+ zs2 is given by the generator matdx[lolrolc=t I

L0 l 0 l lli) Determine all the code wordsii) Find the associated party - check matrix Hiii) Use it to decode the received words : 11101, 11011.

c. Show that Zs is an integral domain. * rr ,. * *

2of2

(06 Marks)

(08 Maiko

(07 Marks)(05 Marks)

USN

Note: Answer FIVE full questions, selectingatleast TLI/O questions from eoch part.

1 a. Define pointer. With examples, explain pointer declaration, pointer

2a.

b.

c.

3a.

b.

c.

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C function for adding two polynomials represented as

10cs35

Max. Marks:100

and use of

Third Semester B.E. Degree Examination, June/July 2013Data Structure with G

Time: 3 hrs.

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PART_A

the pointer in allocating a block of memory dynamically. 106 Marks)b. Define recursion. Give tuo conditions to be lollowed for successire working ofrecursive

progam. Given recursive implementation of binary's search with proper comments.c. -. (06 Marks)

Define three asymptotia notations and give the asymptotic representation of function 3n + 2in all the three notations and. prove the same fiom first principle method. (08 Marks)

What is a structure? Give three different wals of defining structure and declaring variablesand method of accessing membersof strugtrirrs using a student structure with roll number,name and marks in 3 subjects as meinberp ofthat structure as example. (06 Marks)Give ADT sparse matrix and show with a suitable example sparse matrix representationstoring as triples. Give simple transpose function to transpose sparse matrix and give itscomplexity. (08 Marks)How would you represent two sparse polynomials using array of structure and also write afunction to add that polynomials and store the result in the same array. (06 Marks)

Give ADT stack. and with necessary function. exptain implgmenting stacks to hold recordswith different type of fields in stack. (06 Marks)Give the disadvantage of ordinary queue and how it is solved in circular queue. Explain thesame. Explain with suitable example how would you implement circular queue usingdynamically allocated arrays. (08 Marks)Converttheinfixexpressiona/b-c+dxe-a+cintopostfixexpression.Writeafunctionto evaluate that postfix expression and trace that for given data a:6,b-3, c=1, d:2, e:4.

(06 Marks)

Give the mode structure to create a linked list of integers and write C functions to performthe lollowing :

i) Create a three -node list with data 10.20 and 30ii) Inert a node with data value 15 in between the nodes having data values 10 and 20iii) Delete the node which is followed by a node whose data value is 20iv) Display the resulting singly linted list. (08 Marks)

lists? Write(06 Marks)

b. With node structure show how would vou store the

Write a note on :

i) Linked representation ofsparse matrixii) Doubly linked list.

1of2

in linled

(06 Marks)

b.

. ... c.

c.

8a.

l0cs3sPART-B

5 a. Define a binary tree and with example show array representation and linked presentation ofbinary tree. (06 Marks)

b. Write an expression tree for an expression A/B + C t D + E. Give the algorithm for inorder,postorder and preorder traversals and apply that traversal method to the expression tree andgive the result oftransversals. (08 Marks)

Define a Max Heap. Explain clearly inserting an element that has value 21 for the heapshown in Fig. Q5(c), given below and show the resulting heap. 106 Marks)

6a.

b.

d.(03 Marks)shown in(05 Marks)

l.

7 a. Define the foftiving :

i) Singlti'eirded priority queues

ii) Dolfule ended priority queues

iii) Height -based leftist treesiv) Weight - based leftist treesv) A binomial treevi) Extended binary tree.

nig. Q6(d)

'.'. :

With suitable example, explain leftist trees and give structure of nodes.

(06 Marks)(06 Marks)

What is Fibonacci heap? Give suitable example and give the steps for deletion of node anddecrease key ofspecified node in F - heap. (08 Markg.,,.

What is an AVL tree? Stating with an empty AVL tree perform the following sequence ofinsertions, MARCH, MAY NOVEMBER, AUGUST, APRIAL, JANUARY, DECEMBER,ruLY, FEBRYARY, DRAW the AVL tree following each insertion and state rotation tyreifany for any insert operation. (10 Marks)

b. Define RED BLACK trees and give its additional properties starting with an empty red-block tree insert the following keys in the given order {50, 10, 80, 90, 70, 60,65,62},giving color changing and rotation instances.

2 of2

(10 Marks)

USN

Time: 3 hrs.

Third Semester B.E. Degree Examination, June/July 2013

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c. What is paramterized constructor? Explain the different rrhthods ofpassing arguments to the

Max. Marks:100

(08 Marks)

(04 Marks)overloading is

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latitude values by(08 Marks)

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5a.

b.

6a.b.

c.

d.

7a.

b.c.

8a.b.c.

d.

Object Oriented Programming with G++

Note:. Answer FIVE full questions, selectingatleast TWO questions lfrom each part.

PART-AWhat is a statement? Explain jump statements with syntax.

parameterized constructor with example.

program to find sum of2 numbers, using fiiend.fulctions.What are generic funcrions? Explain with synrax.Write a C++ program to demonstrate the addition of two longitude andoverloading operator.

What is inheritance? Explain the s1'ntax of defining derived classes.

function.c. What is function overloading? Explain with example, why function

imporlant?

What is class? Explain the syntax of class.Mention the itiritrictlons thai are placed on static member functions.

What is inline function? Write a C++ program to find maximum of 2 numbers using inline

10cs36

3 a. What are friend functions? What are the advantages of using friend functions? Write a C++

b.c.

What is copy constructor? When the copy conslructor is employed? Explain with syntax.

Explain protected base - class inheritance, with suitable example. [3: il:ll3

PART-B

Explain when constructors and destructors are executed? Explain the order of invocation ofconstructors and destructors in multilevel inheritance with a suitable program. (t0 Marks)Explain how to pass parameters to base - class constructors, with suitable program.

(10 Marks)

What is virtual function? What is the use of virtual function? Write a C++ program todemonstrate calling ofvirtual function tlrough a base class relevance. 110 Marks;What is pure virtual function? Explain with syntax. (04 Marks)What is an abstract class? How it supports run-time polymorphism? (02 Marks)Mention the diflerences between early binding and late binding. (04 Marks)

what are streams in c++? Mention four built - in streams that are automatically openedwhen a C** program beings execution. (06 Marks)Explain width( ), precision( ) and fil( ) functions. (06 Marks)What are I/O manipulators? List and mention the purpose of C++ I.O manipulators.

(08 Marks)