Computer Science and Information Science 4th semester (2012-June Question
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Computer Science and Information Science 4th semester (2012-June Question Computer Science and Information Science 4th semester (2012-June Question Document Transcript

  • USN 1OMAT41 Fourth Semester B.E. Degree Examination.. June 2012 Engineering Mathematics - lV Time: 3 hrs. Note: Answer FIVE fult questions, selecting A* at least TWO qaestions from each part. i t a PART - A la. Using the Taylors method, find the third order approximar" ,otutiorr.,]---$yffi" problem 9 = *y + I . with y(0) = 0. Consider terms upto foufih degree. (06 Marks) dx b. Solve the differential equation I = -rr under the initial condition y(O) = 2, by using the ox-^tL modified Eulers method, at the points x = 0.1 and x = 0.2. Take the step size h = 0.1 and carry out two modifications at each step. (07 Marks)Yo/ c. Given 9 = *, * y ; y(0) = l, y(0. I ) = l. I 169, y(0.2) = 1.2773, y(o.3)= 1.5049, find y(0.4) dxE= correct to three decimal places, using the Milnes predictor-corrector method. Apply the corrector formula twice. (07 Marks) 2 a. Employing the Picards method, obtain the second order approximate solution of theca following problem at x = 0.2, dv dz I, --:-=x+yzi dxdx =y+zx; y(0)= z(0)=-1. (06 Marks) b. Using the Runge-Kutta method, solve the following = 0- I under the-aJ given condition:EE 1!=.[,*9). l. dx d* )6i i;V {07 Mark9 c. problem |{*:9-Oy ox ox =0, y(0) = l, y(0) = 0.1. Given y(0.1) = 1.03995, y(0.1) = 0.6955, y(0.2) = 1. 138036, y(0.2) = 1.258, y(0.3) = 1.29865, y(0.3) = 1.373. (07 Marks)(r< 3 a. Derive Cauchy-Riemann equations in polar form. (06 Marks) /^) ^)oz b. Iff(zrisaregulartuncrionolz.provethat l+-+lF,rl=r +ltr"[ . I r0TMarks) [d* ay )c. c.Ifw=$+iyrepresentsthecomplexpotentialforanelectricfieldandy=x2_y2 x + y determine the function $. Also find the complex potential as a function of z. (07 Marks)
  • 1OMAT41 kr4 a. Discuss the translormalion ol-w =z-i. (06 Marks) b. Find the bilinear transformation that transforms the points z; = i, zz = l, zt = -l on to the (07 Marks) points wt = l, wu = 0, w,l = co respectively. nz2 +cosrz2 c. Evaluate Jsin dz where c is the circle lzl = 3, using Cauchys integral formula. ! rz - lttz -2) (07 Marks) PART -B5 a. obtain the solution of x2y+ xy+ (x2 - nt)y = 0 in terms ofJn(x) and J n(x) (06 Marks) b E*p..r, f(x) = 1a + 3x3 - x2 + 5x-2 in terms of Legendre polynomials (07 Marks) +l 2 q. Prove that IP. (x) . P,, (x)dx = ,;]1 , m = n. (07 Marks) a. From five positive and seven negative numbers, five numbers are chosen at random and multiplied. what is the probability that the product is a (i) negative numbel and (ii) positive (06 Marks) number? b lt a and B are two events with P(A) = 1, rtut =1, ,,o ,,. B) =+, rind P(A/B), P(B/A), Ptatgl. Pr slAt ana PrA/Br. (07 Marks) c. In a certain college, 4a/o of boy students arild lo/o of gill students are taller than 1.8 m. Furthermore , 600/o of the students are girls. If a student is selected at random and is found taller than 1.8 m, what is the probability that the student is a girl? (07 Marks) a. A random variable x has the density tun.tion pt*r -{Kl :t.". Evaluate K. and I 0. elsewhere find: i) P(x < l), (ir P(l < x < 2), (iiD P(x<2), iv) P(x > l), (v) P(x > 2) (06 Marks) b. Obtain the mean and standard deviation of binomial distribution. (07 Marks) c. In an examination 77o of students score less than 357o marks and 897o of students score less than 60Va marks. Find the mean and standard deviation if the marks are normally distributed. It is given that P(0 < z < 1.2263) = 0.39 and P(0 < z < l47 57) = 043 (07 Marks) a. A random sample of400 items chosen from an infinite population is found to have a mean of 82 and a st;ndard deviation of 18. Find the 95Vo confidence limits for the mean of the population from which the sample is drawn. (06 Marks) U. inite past, a machine has produced washers having a thickness of 0.50 mm. To determine whether the machine is in proper working ordel, a sample of l0 washers is chosen for which the mean thickness is found as 0.53 mm with standard deviation 0.03 mm. Test the hypothesis that the machine is in proper working order, using a level of significance of (i) 0.05 and (ii) 0.01 . (07 Marks) c. Genetic theory states that children having one parent of blood tlpe M and the other of blood tlpe N will aiways be one of the thrse tlpes M, MN, N and that the proportions of these tftes will on u., ou.rug. be | :2 : l. A repofi states that out of 300 children having one M parent and one N parent, 3Oo/o were found to be of tlpe M, 459o of type MN and the (07 Marks) remainder of type N. Test the theory by 1 lchi square) test. ) of )
  • I USN 06cs42 Fourth Semester B.E. Degree Examination, Jlune 2Ol2 Graph Theory and Gombinatorics Time: 3 hrs. Max. Marks: I 00 Note: Answer FIVE full questions, selecting at least TWO questions from each part. PART -A I a. Show that the max number of edges in a simple graph with n vertices is n(n - I )/2 (06 Marks) b. How many veftices will the following graphs have if they contain : i) l6 edges and all vertices ofdegree 4. ii) l2 edges, 6 vertices of degree 3, and other veftices of degree less than 3. (08 Marks) c. Prove that number of vertices of odd degree in a graph is even. (06 Marks) 2 a. Determine the number of vertices, number of edges and the number of regions for each of the planar graph in rhe Fig.Q.2(a)(i) and Fig.e.2(a)(ii) and also verifu that Eulers rheorem for connected planar graph is satisfied. (06 Marks) YO a> !5 Fig.Q.2(a)(i) Fig.Q.2(a)(ii) b. Fina a Hamilton cycle, if exisrs, for each of the graphs shoin in Fig.e.2(b)(i) and .E.i Fig.Q.2(b)(ii). If graph has no Hamilton cycle, determine whether it has a Hamilton path. (06 Marks) a-b de- q I J 5 -.. YF h rlrTs Fig.Q.2(b)(i) Fie.Q.2(b)(ii) !; C. Detemine the chromatic polynomials P(G",7,) and chromatic numbers of each of the Z,! following graphs Fig.Q.2(c)(i) and Fig.Q.2(c)(ii). (08 Marks) * ;.i z Fig.Q.2(c)(i) Fie.Q.2(c)(ii) 3 a. Show that for every tree T = (V, E) if lvl>2, then T hasat leasttwo pendent vertices. ((M Marks) I of Z View slide
  • I 06cs42 b. Suppose that a tree T has two vertices of degree 2, four vertices of degrce 3 and three vertices of degree 4. Find the number of pendent veftices in T. (06 Marks) c. What is a prefix code? Construct an optimal prefix code for the symbols a, b, c, .... i, j that occurin agiven sample with respect to frequencies 78, 16,30,35, I25, 31,20,50,80,03. ( 10 Marks) a. Explain Prims algorithm for finding shortest spanning tree ofa weighted graph. (08 Marks) b. Define the following with respect to bipartite graph G = (V, E) : i) Complete matching ; ii) Maximal matcing ii) Deficiency of graph C. (06 Marks) c. Define : i) Cutset ; ii) Edge-connectivity ; iii) Vertex - connectivity with one example for each. (06 Marks) PART - B 5 a. State two basic counting principles. Give on example for each. (06 Marks) b. A committee of 4 is to be chosen out of 6 Englishman, 5 Frenchmen and 4 Indians, the committee is to contain one of each nationality i) In how many ways can it be done? ii) In how many arrangements will a paticular Indian be? (08 Marks) c. Consider the following program segment, where i,j and k are integer variables fori:=lto20do forj:=ltoido for k := I toj do print(i *j + k). Detemine how many times the print( ) statement is executed in above program. (06 Marhs) 6 a. In how many ways can these integers 1,2,3,....., l0 be arranged in a line so that no even integer is in its natural position. (06 Marks) b. Determine the number of positive integers n where I < n < 100 and n is not divisible by 2, 3, or 5. (08 Marks) c. A board consists of the shaded part as in the Fig.Q.6(c). Find its Rook polynomial. (06 Marks) (/Ar/t //, //r /// Fig.Q.6(c) ,4 U, 74. Determine the coefficient of x8 in (x - 3Xx - 2)? (08 Marks) b. Find the generating function for each of the following sequence : it 0,2,6, 12,20. 30.42....... ii) 8.26.s4.92........ (06 Marks) c. Find a formula to express 0r + ll + 22 + ..... + ,l as a function of n, using summation operator. (06 Marks) 8 a. Solve the relation Fn*2 = Fn+r + Fn, where n 2 0 and Fo = 0, Ft= 1. (06 Marks) b. Using generating function, solve yn+:-4yn+r +3y,=0 given thaty6= 2.yt=4. (08 Marks) c. Find the generated solution of S(K)-35 (K- l)-45 (K-2)=4K where K>2. (06 Marks) 2of2 View slide
  • USN 10cs43 Fourth Semester B.E. Degree Examination, Jurre 2012 Design and Analysis of Algorithms Time: 3 hrs. Max. Marks: 100 Notez Answer FIVE full questions, selecting at least TWO questions from each part. E -g PART -A E I a. If tr(n) e 0 (gr (n)) and t2 (n) e 0(gz (n)), prove that rr(n) + r2(n) e 0(max {gr(n), g:(n)}). (06 Marks) b. If M(n) denotes the number of moves in tower of Hanoi puzzle when n disks are involved, give a recurrence relation for M(n) and solve this recurrence relation. (07 Marks) c. Give an algorithm for selection sort. If C(n) denotes the number of times the algorithm is;> executed (n denotes input size), obtain an expression for C(n). (07 Marks);r. ,^ 2 a. Assuming that n is a power of 2, solve the recurence relation T(n) = 2T(nl2) + 2. Take T(2) = 1 216 111; - O. (0s Marks)E b. Ifne[2k-1,21), prove that binary search algorithm makes at most K element comparisons for a successful search and either K - I or K comparisons for an unsuccessful search. (06 Marks)aa c. Give an algorithm for merge sort. (05 Marks)ic d. Consider the numbers given below. Show how partitioning algorithm of quick sort will placei9 106 in its correct position. Show all the steps clearly. 106 17 128 134 141 91 84 63 42. (04 Marks) 3 a. Let J be a set of K jobs and o= ir, iz, i:,......., i1 be a permutation ofjobs inJ such that dir < di: < ....... 3 dir,. Prove that J is a feasible solution if and only if the jobs in J can be (07 Marks) . processed in the order o without violating any deadline.iatrc b. Using Prims algorithm, determine minimum cost spanning tree for the weighted graph shown below, fig.Q.3(b): (07 Marks) d8_ e+ i9 ae :p * ;>J< Fie.Q.3(b)J.i c. In the weighted digraph given below, fig.Q.3(c) determine the shortest paths from vertex I to all other vertices. (06 Marks)z E
  • 10cs434a. Obtain the shortest paths faom every vertex to every other vertex in the diagraph given below; fig.Q.4(a) (10 Marks) Fig.Q.4(a) b. Using Warshalls algorithm, obtain the transitive closure of the matrix given below: [o r o or *=lO n n nl lo n ,l rr0Marks) tl 0 n 0i (r r PART-B5a. Show how insertion sort algorithm arranges the following members in increasing order. 61 28 9 85 34. (06 Marks) b. (06 Marks, Fig.Q.s(b) c. Give algorithms for the following: i) Comparison counting; ii) Distribution counting. (08 Marks)6a. Define the following: i) Tractable problems; ii) Class P; iii) Class Np; iv) polynomial reduction; v) NP complete problems. (05 Marks) b. State subset sum problem. Using back tracking, obtain a solution to the subset sum problem by taking s = [6, 8, 2, 14] and d = 16. (07 Marks) c. Explain approximation algorithms for NP - hard problems in general. Also discuss approximation algorithms for knapsack problem. (08 Marks)7 a. What is prefix computation problem? Give the algorithms for prefix computation which uses .. ... i) n processors; ii) n processors. Obtain the time complexities ofthese algorithms. tog n - (10 Marks) b. For an n xn matrix M with nonnegative integer coefficients, define ft and give an algorithm for computing ,I . Prove that ft can be computed from an n x n matrix M in 0(log n) time using n3* common CRCW PRAM processors for any fixed e > 0. (10 Marks) Write short notes on: a- Traveling salesperson problem. b. Input enhancement in string matching. c. Decision trees. d. Challenges of numerical algorithms. (20 Marks) 2of2
  • USN 10cs44 Fourth Semester B.E. Degree Examination, Jurl,e?Ol2 Unix and Shell Programming Time: 3 hrs. Max. Marks:100 Note: Answer FIVE full questions, selecting at least TWO questions from each part. PART -A 1 a. With neat diagram, explain the architecture of unix operating system. (06 Marks) b. With the help of a diagram, explain the parent-child relationship. Explain the unix file system. (06 Marks) 2 c. Explain the following with examples: i) Absolute and relative path names ii) Internal and extemal commands. (08 Marks)*= 2 a. A files current permissions are rw_r_xr__. Specify the chmod expression required to change them for the following: i) rwx rwx rwx ii) r__ r__ ___ iii) ___, iv)___ r__ r__ using both the relative and absolute methods of assigning permissions. (08 Marks)go) b. Explain briefly the file attributes listed using ls - I command. (06 Marks) c. What are the different modes of Vi editor? Explain with a diagram. (06 Marks) 3 a. Explain the thee standard files with respect to unix operaring syste;lff. ; - , . (06 Marks) b. Expiain the mechanism of process creation. * ,.. --.- : ^ r.-(06 Marks) - c. Explain the following commands with an example, 1, . , i) Running jobs in bickground ii) Execute Lter. ,i " -,.,,., , ; fua uarks) :. >i 4 a. Explain the Iollowing environment variables with examples: (.1**". . .Z2- DSHELL ii)LOGNAME ii|PATH 1-!:i* (06Marks)o. 5-o- b. Differentiate between hard link and soft link in unix with examples. (06 Marks)o; c. Explain the following commands with example: i) tail ii) paste iii) tr iv) pr (08 Marks) PART - B 5 a. With suitable examples, explain the grep command and its various options. (08 Marks) b. Explain the line addressing and context addressing in sed with examples. (06 Marks)-> c. Explain the different ways of using test statements, with examples. (06 Marks)Q< 6 a. What is shell programming? Write a shell program that will do the following tasks in order: Clear the screenz Print the current directory Display current login users. (08 Marks) b. Explain the shell features of while and for with syntax. (08 Marks) c. What is the exit status of a command and where is it stores? (04 Marks) I ,)
  • 10cs44 a. What is AWK? Explain any three built in functions in AWK. (07 Marks) b. Write an AWK sequence to find IIRA, DA and Netpay of an employee, where DA is 25Vo of basic, HRA is 50% basic and netpay is the sum of HRA, DA and basic pay. (07 Marks) c. Explain the list and anays in PERL. (06 Marks)8 a. Explain the following storing handling functions of PERL with examples: i) length ii) index iii) substr iv) reverse (08 Marks) b. Write a PERL pro$am to pdnt numbers that are accepted from keyboard using while and array construct. (06 Marks) c. Explain the following in PERL with examples. i) fore each loping constnrct ii) join (06 Marks) ***** 2 of2
  • USN 10cs4s Fourth Semester B.E. Degree Examination, Jlurrre 2O1^2 Microprocessors Time: 3 hrs. Max. Marks:100 Note: Answer FIVE full questions, selecting at least TWO questions from each part. c. s PART-A 1a. Describe the memory map of a PC system, with a neat diagram. (0E Marks) b. Explain the flags of 8086 processor using suitable examples. (06 Marks) c. Draw_and explain the programming model of the g0g6 through the coRE-2 microprocessor including the 64-bit extensions. (06 Marks)-*ll 2a. What are the advantages of memory paging? Illustrate the concept of paging with a neat,EA diagram. (10 Marks)tso b. Discuss the following addressing modes with examples: i) Direct ii) Regisrer indirect ii, Base plus index iv) Immediate v) Scaled indexed. (10 Marks) 3a. Describe the following instruction with suitable examples: i) PUSH ii) MUL iii) IN iv) AAA. (08 Marks) b. Write an ALP using 8086 instructions to generate and add the first l0 even numbers and.i save the numbers and result in memory location Num and Sum. (08 Marks)e- c. Bring out the importance of XLAT instruction using a suitable program. (04 Marks):., 4a. write an ALP using 8086 instructions to count the numbers of zeros in a given g bit number and store_the result in memory location ,Res,. (08 Marks) b. Explain the following assembler directives: i) Assume; ii) proc; iii) Ends; iv) DB. (08 Marks) C, Briefly explain any four bit test instructions. (04 Marks) PART - Bd>(r< 5a. Explain public and extrn directives of assembler and write ALp to read data through k-eytoard using external procedure and save the keycode in public data segment. (08 Marks) b. write a c program that uses -asm function to display strings on output device. (06 Marks)z c. Explain with neat diagram clock generator IC82g4. (06 Marks)c 6a. Explain in brief the funcrions of 8086 pins: it MN/MX: ii) ALE; iii) NMI; iv) Ready;E v) Reset; vi) BHE-. (06 Marks) b. Describe demultiplexing of multiplexed AD bus with neat diagram. (06 Marks) C- With neat timing diagram, explain memory read cycle. (08 Marks)
  • 10cs4s7a. Interface 512 KB RAM to 8088 MP using 64 KB RAM using 3:8 decoder with starting address of memory as 80000H. Clearly mention decoding logic and memory map. (08 Marks) b. Explain memory bank selection in 8086 and mention the number of memory bank in 80x86 MPs. (06 Marks) c. Differentiate between memory mapped I/O and I/O mapped I/O (isolated I/O). (06 Marks)8a. Interface 8 digit seven segment LED display to 8088 MP through 8255 PPI. Write initialization sequence for 8255 with all port as output ports in mode 0 and address of device is FFOOh- (08 Marks) b. Explain control work format for IC 8254 and interface IC to 8086 MP to generate square wave of 100 kHz using counter 0 write an ALP for the same. Assume clock frequency of l0 MHz. (08 Marks) c, Explain intemrpt vector table in brief. (04 Marks) 2 of2
  • V USN 06cs46 Fourth Semester B.E. Degree Examination. June 2Ol2 Gomputer Organization Time: 3 hrs. 100 Notet Answer FIVE full questions, selecting :e? "7-O :/Ff .:* j-. at least TWO questions from each paq$^;Yrr..-iN4 ,,rl /df t<f PART_A i 1a. Define and explain briefly the following : ,.{ "_rrit-:r" j " "r"rr; " .*r;1": i) rate l) ( toct( rate Clock I) L tSL ii) CISC ri.., ,!.,;, iii) RISC iv) Basic performance equation. - . -,--{-1)@ -fii uartrsr b. Describe the basic functional units of a computer with a neat diagram. !---. - - - (08 Marksr - 2a. What are generic addressing modes? Write down the assembler syntax and addressing function. (I0 Marks) b. Explain the following with reference to subroutines : i) Subroutine nesting and the processor stack ; ii) Parameter passing ; iii) Stack frame. zr) (10 Marks) ,Ed 3a. What is an exception? Describe the different kinds of exception. (10 Marks) b. How do you enable and disable interrupts? (05 Marks) E9 c. Define privileged instruction and explain how privilege exception occurs. (05 Marks) fre 4a. Explain the use of a PCI bus in a computer system with a neat sketch. (08 Marks) b. Draw the diagram of universal setial bus tree structure. (04 Marks) c. Define the following : i) Serial port ii) Parallel port iii) SCSI iv) USB. (08 Marks) -E ca PART-B 5 a. Draw a neat block diagram of memory hierarchy in a computer system. Discuss the variation .of size, speed and cost per bit in the hierarchy. ni b. What are static and dynamic RAMS? Explain. (07 Marks) (05 Marks) C. Define memory latency and bandwidth of a synchronous DRAM memory unit. (04 Marks) eg d. Define and explain the following : i) Static memories ii) Memory access time iii) p414 iv) Memory cycle time. (04 Marks) EE 6a. Draw the block diagram of virtual memory organization. !* (04 Marks) b. Explain the virtual - memory address translation with a neat diagram. (10 Marks) c, Discuss the organization and accessing of data on a disk. (04 Marks) d. A 3.5 inch (diameter) high-capacity, high-data-rate-disk has the following parameters. There a- are 20 data-recording surfaces with 15000 tracks per surface. There is an average of400 sectors per track and each sector contains 512 bytes of data. Calculate the total capacity of formatted disk. (02 Marks) z 7a. Discuss Booth algorithm by multiplying the numbers -13 and +l l. (08 Marks) b. Explain bit pair recoding technique by multiplying the numbers +13 and -6. (06 Marks) E c. Explain restoring division using a 4-bit example. (06 Marks) 8a. Draw the three-bus organization of the data path and describe in detail. (10 Marks) b. Witha neat sketch, explain the basic organization of a micro programmed control unit. (10 Marks)
  • USN 10cs46 Fourth Semester B.E. Degree Examination, Jane 2Ol2 Gomputer Organization Time: 3 hrs. Max. Marks:100 Note: Answer FIVE full questions, selecting atleast TWO questions frorn each part. PART -A 1 a. What is performance measurement? Explain the overall SPEC rating lor the computer in a I program suite. (04 Marks) b. List and explain the technological features and devices improvement made during different generations of computers. (08 Marks) c. Mention four types of operations to be performed by instructions in a computer. Explain with basic types of instruction formats to carry out C <- [A] + [B]. (08 Marks)-0, ll 2 a. Define an addressing mode. Explain the following addressing modes, with example : immediate, indirect, index, relative and auto increment. (10 Marks) b. What is a stack frame? Explain a commonly used layout for information in a subroutine stack frame.o c. Explain shift and rotate operations, with example. (10 Marks)?idoJ 3 a. In a situation where multiple devices capable of initiating interrupts are connected to processor. explain rhe implementation of interrupt priority, using individual TNTER and INTA and a common INTR iin. to all devices. (10 Marks)-o b. Define the terms cycle stealing and block mode. (02 Marks) c. What is bus arbitration? Explain the different approaches to bus arbitration. (08 Marks)-r) C^9= 4 a. Explain with a neat block diagram, the hardware components needed for connecting a keyboard to a processor. Marks) (0E b. Briefly discuss the main phases involved in the operation of SCSI Crr, (06 Marks) c. Explain the tree structure of USB with split bus operation. <:"4 06 Marks);i PART-B!9 5 a. Explain the intemal organization of a 16 megabit DRAM chip, x 8 cells. (08 Marks)lr< b. With a block diagram, explain the direct and set associative mapplng cache and-i c.i main memory. (06 Marks)o c. Describe the principles of magnetic disk. (06 Marks)z 6 a. Explain with figure the design and working of a 16-bit carry - look - ahead adder built form 4-bit adders. (06 Marks) b. Explain Booth algorithm. Apply Booth algorithm to multiply the signed numbers +[3 and -6. (10 Marks) c. Differentiate between restoring and non-restoring division. (04 Marks)
  • 10cs467 a. List out the actions needed to execute the instruction add(Rr), Rr. Write and explain same. sequence of control steps for the execution of the (10 Marks) b. With a neat block diagram, explain hardwired control unit. Show the generation Zin andBnd control signals. (10 Marks)8 a. State Amdahls law. Suppose a program runs in 100 sec on a computer with multiply operation responsible for 80 sec of this time, how much it requires to improve the speed of multiplication, if the program has to run 5 times faster? Justify your answer (06 Marks) b. Explain the classic organization of a shared - memory multiprocessor. (06 Marks) c. What is hardware multithreading. Explain the different approaches to hardware multithreading. (08 Marks) 2of2