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- 1. € C I .I USN lOMAT3I Max. Marks: L00 (07 Marks) (06 Marks) (07 Marks) (07 Marks) (07 Marks) Third Semester B.E. Degree Examination, June/July 2013 Engineering Mathematics - lll Note: Answer FIVE full questions, selecting t leasl TWO questions from each part. a C9 =rl-^i Etr t.- ;B ,o $o (r< :' o z o PART - A [ *- il 0<x<n I 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 y from 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 the method 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 a x 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 f Subject 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)
- 2. 5a. b. -- c. 1OMAT31 PART - B Using 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 73.9 b. 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 > 0 A Ax' 7-ordinates and hence find log.2. (06 Marks) (07 Marks) (07 Marks) (06 Marks) c. Evaluare f--I- a* bv weddle's jl+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
- 3. r- { USN 06ES32 (05 Marks) Determine: i) r"; ii) Z; ' (07 Marks) Time: 3 hrs. Third Semester B.E. Degree Examination, June/July 2013 Analog Electronic Gircuits Max. Marks: 100 Notez Answer FIVE full questions, selecting at least TlltO questions from each part. PART - A I a. What do you understand by reverse recovery time? Explain it, which is applicable to diode circuit. (05 Marks) b. Explain the working of centre tapped full wave rectifier circuit using diodes. Compare it with 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 Vg6 on 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: E E9 .E& fr= -.. r o.v t.) -;o ; z o E v,, '' L[--o* v; Vc. (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
- 4. 5 ,a. b,' 4a. b. c. 6a. b. c. c. 8a. b. c. 06E532 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 the equation of input and output capacitances. (10 Marks) PART-B Explain the cascade connection of general amplifier with the help of block diagram. write its advantages. (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 maximum conversion 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) 2 of2
- 5. USN 06cs33 (08 Marks) (08 Marks) (04 Marks) (05 Marks) (05 Marks) Third Semester B.E. Degree Examination, June/July 2013 Logic Design a I E9 gor "5 -bi 5r o.a d; d .9. a! a,i :s -;o o z 6 ts q E Time: 3 hrs. .':.. Max. Marks:1O0 Notez Answer FIYE full questions, selecting atleast TWO questions lfrom each part. PART_A I a. Why NAND and NOR gates are universal gates? Simptifo the following Boolean expression using k - map and implement the same using i) 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 and external 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+38 ii) 8r6 + Fr6. a. What is a fliplfop? Explain the different types of flipflops diagram, 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
- 6. r1 I06cs33 6 a. Differentiate Mealy and Moore models. (05 Marks) b. Design an aslmchronous sequential logic circuit for the following state transition diagram. I _ (05 Mar(5) -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. ,lr /o 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<g r{* ""f I ***rr* -t'lt. '.''a&* 2 of2 Fie. Q6(b)
- 7. USN 06CS/IS34 (08 Marks) (06 Marks1 Time:3 Third Semester B.E. Degree Examination, June/July 2013 Discrete Mathematical Structures hrs. Ma.x. Marks: r oo Note: 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 that A-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, roller coaster and Ferri's wheel. It is known that 20 of them have taken all the 3 rides and 55 of them have taken atleast 2 ofthe 3 rides. Each ride cost Rs. 0.50 and the total receipt of the amusement park is Rs. 70. Determine the number ol children who did not try any of the three 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. o E 3P ih.^t .E . Y.J ?^ .ed *q d .9. AE 3U (.) < .i .i o z E la. b. t^ b. p-+q r 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 negation i) If all triangles are right angled, then no triangle is equiangular ii) 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, r i) [(p " q) -+ r] <> t(p] 0 a (q -+ r)l ii) [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 method ii) Indirect method iii) Contradiction merhod. I of 2 (06 Marks)
- 8. 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 prove t,,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>2 ii) 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 ll i) Determine all the code words ii) Find the associated party - check matrix H iii) 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)
- 9. USN Note: Answer FIVE full questions, selecting atleast TLI/O questions from eoch part. 1 a. Define pointer. With examples, explain pointer declaration, pointer 2a. b. c. 3a. b. c. /^ C function for adding two polynomials represented as 10cs35 Max. Marks:100 and use of Third Semester B.E. Degree Examination, June/July 2013 Data Structure with G Time: 3 hrs. u o E g# n^ 5o .9 63 A; 6E :ll rJ< ; a z ts o s 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 + 2 in 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 variables and 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 representation storing as triples. Give simple transpose function to transpose sparse matrix and give its complexity. (08 Marks) How would you represent two sparse polynomials using array of structure and also write a function 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 records with different type of fields in stack. (06 Marks) Give the disadvantage of ordinary queue and how it is solved in circular queue. Explain the same. Explain with suitable example how would you implement circular queue using dynamically allocated arrays. (08 Marks) Converttheinfixexpressiona/b-c+dxe-a+cintopostfixexpression.Writeafunction to 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 perform the lollowing : i) Create a three -node list with data 10.20 and 30 ii) Inert a node with data value 15 in between the nodes having data values 10 and 20 iii) Delete the node which is followed by a node whose data value is 20 iv) 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 matrix ii) Doubly linked list. 1of2 in linled (06 Marks)
- 10. b. . ... c. c. 8a. l0cs3s PART-B 5 a. Define a binary tree and with example show array representation and linked presentation of binary 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 and give the result oftransversals. (08 Marks) Define a Max Heap. Explain clearly inserting an element that has value 21 for the heap shown 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 trees iv) Weight - based leftist trees v) A binomial tree vi) 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 and decrease key ofspecified node in F - heap. (08 Markg.,,. What is an AVL tree? Stating with an empty AVL tree perform the following sequence of insertions, MARCH, MAY NOVEMBER, AUGUST, APRIAL, JANUARY, DECEMBER, ruLY, FEBRYARY, DRAW the AVL tree following each insertion and state rotation tyre ifany 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)
- 11. USN Time: 3 hrs. Third Semester B.E. Degree Examination, June/July 2013 4a. b. c. E E tje -*l '=+ Y!, Cz tro- orro z o 1a. b. 2a. b. c. What is paramterized constructor? Explain the different rrhthods ofpassing arguments to the Max. Marks:100 (08 Marks) (04 Marks) overloading is (08 Marks) (08 Marks) (04 Marks) (08 Marks) (08 Marks) (04 Marks) latitude values by (08 Marks) (08 Marks) 5a. b. 6a. b. c. d. 7a. b. c. 8a. b. c. d. Object Oriented Programming with G++ Note:. Answer FIVE full questions, selecting atleast TWO questions lfrom each part. PART-A What 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 and overloading 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 of constructors 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 to demonstrate 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 opened when 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)

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