O6MAT41USN

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5 t a. EmdTOlTaylor's series method to find an approximate solution confrqt to fourth decimal6d-

E place, dffi :2y + 3e', y(0) :0 at x: 0.1 and x :0.2. r ** (07 Marks)E,d,Oltt'\E .;.::-:::;::4 - - dv lxl .. ,li-,.'

Fourth Semester B.E. Degree Examination, June/July 2Ol4Engineering Mathematics - lV

,i.,,'.Time: 3 hrs. Max. MarkqrlpCI'Note: Answer FIVE full questions, selecting

' ",, at least TWO qontioot from each pirt. ':""i .

li;.r.,(D ,,.':,, .::'o

gi b. using *"iii*t *'s method, solve * = "r,,(l W&f : t at x : 20.2 and 20.4

t 5 by taking h: 0.2. (07 Marks)

F"? r. dv ,}0+ c. Using Adams - nashibitk;method, frnd y whenif-"+ O.A given *=*-y', y(0):0,E $ "p-; dx

E g. y(0.2):0.02, y(0.4) : 0.079$tqMJ y(0.6) : a.1762. (06 Marks)

€EE

= '*r"*'

9 g 2 a. Define analytic function. Derive CAtffiftiemann equations in polar form. (07 Marks)"

"l ""!*

A E b. Find an analyic function (r) : g'&#, iT**,=_ v : e'(cos y - sin y) (07 Marks)ET<q *l

E S c. Discuss the transformation w.l z +: (z + 0). "

i,,," "-, (06 Marks)o!50- Z(,d

:b IE E 2 a Qfofo o-r{ ht'nr,^ r-o"^L\h,'i-tanrcl f^.mrrlo /nt tt,rd'tz.\E E 3 a. State and prove Cauoh}ft integral formula.(, rd - s .@hts -r-hC t- r

€ € 3 a. State and prove Cay*Qffre integral tbrmula. (07 Marks)

-hr q E / 1

E: b. Expand flz) :&ffi -62{ in a Laurent's seriesT; rrrc region (i) 2 < I z I < 3,

trdE $ (ii) 3 < I x'*.4l < s. qfu (07 Marks)a9-sH'E ?-3t) ,r'.=a9.sU€ --.\ - e 323+2 {'eE c. Usirig.€auchy'sresiduetheoremevaluate, {, ..,, ^,wherec:lt'"fi,p4. (06Marks)E .E e theorem evaluate, |ffi, where c: lz[;4'

t-(l){i

x:E' ;. 4 a." Obtain the series solution of 'r'll '! *.

*",,l,,=

cd \*qg g 1 .i {'. xry: o (07 Marks)Fs dx'o-s- al "" I

@=< -' b. Showthaty:xnJn(x)isasolutionofthedifferentialequationxy"+(1 -2n)y'*xy:0 *'ffiir'-..i t i

; (07 Marks)i -- press (x) : xo + 3x3 - rJ + 5x - 2 in terms of Legendre's polynomials. (06 Marks)2 c. -trx

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I of2

O6MAT41

5a.

ui" b'

..:. ',r i

PART _ B

Derive normal equations for fitting a straight line y : a ! bx by the method of least squares

and hence explain the method of fitting the curve y : a eb' . (07 Marks)

Find the coefficient of correlation and the lines of re n for the data

::. ,, ,i.

A randofuihriable X has babilit tu.....",,,]]l

t.,r'

in" reports. The probabilities that they misfile such reports are re_spec$iwty.'0.05, 0.1, 0.1

XnS. nina the probability that a misfiled report is caused by the first se&etary. (06 Marks)Find the probability that a misfiled report is caused by the first I

S :'r ':

6a.

7a.

b.

the followins probability function:x 0 I 2 3 4 5 6

P(x) 0 k 2k 2k 3k k" 2k' "7k'+ k

b.

c.

(07 Marks)

(07 Marks)

with a mean of 3

(ii) takes between(06 Marks)

Explain the following terms:

6 marks. Could this have b.., u random ,u-pi. fr'omo;population with average marks 50?

(Use 5% level of si nce). (07 Marks)

c. A certain st

(i) Null hypothesis (ii) Level of significarrce (iii) Type I and II effors. (07 Marks)" . r.{

The average marks in md&Gmatics of a sampl&tif 100 students was 51 with a S.D. of

{hded that the stimulus will'-q

* (06 Marks)

'\8 a. A fajf,$in is tossed tlrice. The random variables x and y are defined as''fsllows:

4x :or 1 according as head or tail occurs on the first toss. y: Number of heeds. Determine

,,;(i)'ihe distribution of x and y (ii) the joint distribution of x and y (iii) the expectations of..,,,.1. 'x, y and xy (iv) Covariance and correlation of x and y. (07 Mart<g

"1fe 6. Define stochastic matrix. Find the unique fixed probability vector for the matrix. '-,,.;'''-;,-

\d (o 1 o') *_\d (o 1 o) ^r_='"':,=r',n ltta Uz tl3l (o7Markdff,*t''"^'-l"tt

[ 0 2t3 U3)

c. A software engineer goes to his office everyday by motorbike or by car. He never goes bybike on two consecutive days, but if he goes by car on a day then he is equally likely to go

by car or by bike the next day. Find the t.p.m. of the Markov chain. If car is used on the firstday of the week, find the probability that after four days (i) bike is used (ii) cars is used.

*,r r r * t06Marks)

2 of?

MATDIP4OlUSN

I of2

6 a. Find Laplace Transform if t' and hence ftrd L[t;).

b. Find L[e" cos3t + e-' sin zt + t sin t] .

MATDIP4Ol

(06 Marks)

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(10 Marks)

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4F.

Z *%.*+ind L[sin t sin 2t sin 3t].

%*.t'*1.

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I vs-qJ1=rr,g*"\, 1..

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USN 10cs42

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

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at least TWO questionsfrom each parlPART-A ,,.."""'ri

Fourth Semester B.E. Degree Examination, June / July 2Ol4Graph Theory & Gombinatorics

Time: 3 hrs.

0)C)

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a. Let G be a simple graph of order n. If the size of G is 56 and the size of G it 80, what is n?

': ' '(05 Marks)b..'Define isomorphism of graphs. Show that the following two graphs in Fig, Ql (b) are

i'scrmorphic .q, = (05 Marks)%# x .A.t$t;r, G, where removing any

edge e results in an disGonnected graph. (05 Marks)d. Diicuss K0nigsberg bridgoproblem. (05 Marks)

a. Define Hamilton cycle. "O'+

E) is a loQf free undirected graph wittr lVl = n ) 3 and if

p1=[",').,,thenproveth"t6 iltoncycle. (06Marks)

b. Define planar graph. If a connpale{ltffiar graph G has n vertices, e edges and r regions,

then prove that n -e -tr =2. (07 Marks)c. Define chromatic number. Fio'd the chromatiC iloly-aomial for the cycle of length 4. Hence

find its chromatic number. 1'"i- (07 Marks)

''-," , , {i;",a. Define a tree. P.o.-rf, in a tree T = (V, E), lvl = lfl+\'.'=ryt (06 Marks)

ord;gxern.ple for each. Find all thespanning tre.qsbf the graph as shown in Fig. Q3 (b) -.{:.:: (07 Marks)

c. Construct-fuhoptimal prefix code for the letters of the word ENGffi$ING. Hence deducethe co($$i this word. " " ",fl (07 Marks)

a. pg e : i) Edge-connectivity ii) Vertex-connectivity and iii) Complete'ftratshing. Give an

.r.'OXample for each. (06 Marks), h,, State Kruskal's algorithm. Apply Kruskal's algorithm to find a minimal spanning free for the''','i following weighted graph as shown in Fig. Q4 (b). $7man<9

bs-atLC :".':::' .i ''::.uj'tfu,.

Fig. Qa (c)Fig. Qa (b)

State Max-flow and Min-cut theorem. For the network shown below in Fig. Q4 (c), find thecapacities of all the cut sets between the vertices A and D, and hence find the maximum

flow.I of2

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Fourth Semester B.E. Degree Examination, June / July 2Ol4Microprocessor

, Time: 3 hrs. ,i l,aarfi,"}l0t

imi, Answer any FIVEfutl questions, selecting atleast TWO questionsfrom eac..h'nart..r,1."' ,,:' ,,,,1", PART - A -' ;:;

1 a.;*W,:th a neat diagram, explain the architecture of 8086 microprocessor alo$l yith functionsMiegch block and register. ,:. .". (12 Marks)

b. What--is.an addressing mode? Explain any 3 addressing modes, with'examptir:fr."X*;

a. Write and eap-lain instruction template for MOV instruction Sbe"$enerate opcode for thef^lr^---:-- i;:*;-,-^+i^-^ r.\.^^^l^ C^- I\/f,.\\/ :^ ".tr, i I /in n[^-r.-\following inStructjons. Opcode for MOV is

100010i) Mov BL, cL $ IIvIOV [Sr], DL iii) MOV CX,',[437A H] iv) MOV CL, [BX]

b. Write 8086 assembly,ing$ruction which will perforrrqthe following operations :

D Load the number 34tintq.4L in hexa. '"'::'''

ii) Divide the AL register conpnts by 4 using,shi'ft instruction.iii) Multiply the AL register Corrtents by 2 qs'iry=shift instruction.iv)Whichoftheflagsaresetwhe-@pse,jri$iuctionsareexecutedifAL:10010101

BL:0 0 1 0 1 1 0 l. ADB-AL, BL and CMP AL, BL. (05 Marks)

c. What is the result after executionoftlrese instructions ifAL : 0 1 1 0 1 1 1 0 CF : 1

i) SHR Al, 0l ii) ROR AL, 01 iii) SAL AL, 01 iv) RCL AL, 01

v) ROL AL, 01. (05 Marks)

Explain the different types$flrnconditional jump ffiructions. (10 Marks)Write an ALP to calcu delay of 100msec for'{p86.microprocessor working at 10MHzclock. Assume and medon the states for each instructii$ffiused. (06 Marks)Write an ALP to-fih*{he factorial of a 8 bit number (04 Marks)

Differentiate beiulben macros and procedures. (05 Marks)

Explain cpqlgl_me string (CMPS) instruction, with an example. ' ..;_ (05 Marks)

write au r{Ep to reverse a given string

IJ.::-t ther it * n ntffi'ro,i*

Marks)

.B,1 lain the following instructions, with an example : i) DAA ii) DIV -;iiD SCASBiv) IN v) PUSH. ;,(lo Marks)What is an assembler directive? Explain the following assembler directive, with $1e;gample.i) PUBLIC ii) ASSUME iii) EQU iv) EXTRN. fl0adarks)""

"'"' """'

With a neat diagram, explain the pin configuration of 8086. (10

Write the timing diagram for a memory read machine cycle of 8086. (05 Marks)Explain how 8088 microprocessor accesses memory and ports. (05 Marks)

With a neat diagram, explain interrupt vector table along with Type 0 to Type 4 interrupts.(10 Marks)

Briefly explain the ICW's formats of 8259. (10 Marks)

Explain the different methods of parallel data transfer with figure in a programmableperipheral interface. (10 Marks)

b. Explain in detail the software keyboard interfacing with circuit connection and algorithm.(10 Marks)

**rtrr*

::,,,,.,,,:,,, 11000101 lr-\'-D MOV BL, CL iCI',,MOV [SI], DL iii) MOV CX','[AE7AH] iv) MOV CL, [BX]

3a.b.

c.

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Fourth Semester B.E. Degree Examination, June/July 2014UNIX and Shell Programming

s lime: 3 hrs. Max. Marks:1OO;''.-. ''i'; Note: Answer FIWfull questions, selecting 'i"*'\"'i""'"'O ':'i.i,ra-'- r' i'':" ':' atleast TWO questionsfrom each part. .'tI '4rr ,# J -i;A ' lq,I(BLo-(6 ^ ^ ^-E PART_Aj :,:#\* il.tfutt d &.e tu e

f; 1 a. Wffigeat diagram, explain the architecture of UNIX operating sysf;eiii%IJist the featureso,ns.i also. Lri*

". 'dffi (08 Marks)

o, *rDv. "ry#q\ .+4 4fl, "

: b. Explainqtku.parent-child relationship of UNIX file system with a*-@-.i4fum. (06 Marks)r - phin wib&€xamPles : *fl 8 "'-"\- ,i*t7 c. .bxplam wlmexamples :>^ c. Exprarn wlr*J9l@mples .

J il"3 i) Absolute pathname and relative pathname -,; "rr ..i - "\*rr ..1 ^ ^--"^"1- r**i41i--- ' - r----------- .,

-t %".foo ll) lnternal and e*ternal commands. (06 Marks),-; {? tt) lllttrIllill auu (id$trlbllal uullllllallLtJ. *, \ =" tuu lvr4rnD.,r

Ar ' fl""'<t

B' 2 a. Interpret the significanee pf seven fields of .ts -.[ ou{fu. (07 Marks)

.E b. Briefly explain the differeni ways of setting file perml'ssions. (07 Marks)i c. With a diaeram. exolain 3 niry 3s of Vi editor*, l (06 Marks)

! c. Explain the following enviro iableS,,with examples :

€ i) HOME ii) PATH iii)TFS iv) SHB'Sff,'^ (04 Marks)JL

made in separate p.o..rr.Explain the following enviro iabi) HoME ii) PArH iiDljs iv)

.e"1,'\E '

; made in separate process. .= %"3'-"'"*" tu (08 Marks)

$ c. Explain the following environnt@[.flariable3,,with examples :

JLE i"">

fr 4 a. What are hard links and:$ft'link? Explain with exalnphr,, (06 Marks)

E b. Write a short note on find command. (06 Marks)b. Write a short note o;r.=fiiid command. "''..

c. Explain the followiXrS filters with examples : q-4a s fi- _ "-'./ e

E i) head ii0 ffi'{ iii) cut. -tr : . (08 Marks)A'1.

o ,, n.:r\,' # -'ari ":"'iaa\4\I U/ .;- ."% qi B &g ._j:"." PART-B *ttr.E ,- l,' '" I ^r\r - s *d -,,..b ".,- k#oo-&.g 5 a. "Exfihin grep command with all options. '* (10 Marks)g bn.-']Vhat is sed? With example, explain line addressing and context addressing. ",qy'"Oo Marks)okh :- 'fi ''r''\,

i 'ffi a. What is shell programming? Write a shell script to create a menu which displays : ' _

" " dffi# * i) List of files ii) Contents of a file iii) Process status *-

***s.-*"1.: * iv) Current date v) Clear the screen vi) Current users of system. (10 Miik*s}.Ii.t rr - , ?.o ! trr"l , 1 I '! b. Explain shell features of 'for'. With syntax and examples. (10 Marksffi;'

7 a. What is an awk? Explain all the built in variables used by awk. (10 Marks)b. With syntax and examples, discuss the control flow statements used by awk. (10 Marks)

8 a. Write a Perl script to demonstrate the use of chop function.b. Write a Perl script to find the square root of command line arguments.c. Explain the string handling functions of Perl with appropriate examples.

10cs43USN

Fourth Semester B.E. Degree Examination, June/July 2014Design and Analysis of Algorithms

s. Max. Marks:l0oi*-,:::::: i},si@-e: 3 hrs'

Note: Answer FrvEfull questions, selecting * u4'

at least TWO questions from each part.n1*#*''

? PART_Ao !q' J,l$

'-: )

I I a. O.f,pryu three asymptotic notations. ., {,),' .,,.',"" (06 Marks)€ "t*"*' &" +H U. Ded'ftr$a recursive algorithm for solving tower of Hanoi problem and gi{e the general plana-fi of ana$Liag that algorithm. Show that the time complexity of to_w.e-r,8f Hanoi algorithm isrD-E exponential,irqnature. .\" (08 Marks)

gg c. With algoritfrn"and a suitable example, explain how tlre-t iie force string matching' ;orithm works. Aualyse for its complexity o\ ", (06 Marks)i5. E AIE

x?-, I5 o L'" fl/.-\A? 2 a. Give general 6;ui6s*qf,d conquer recumence with'necessary explanation. Solve theg- oo

= f; recurrence T(n) : 2T(il2) + I

.! (\d r{' T(n) = f(r/2}l#'n t} ^ (06 Marks)H on T(n) : T(n/2) + n, , "h

t=v

E f b. Explain with suitable example'a.Sr,tlng plgorithm that uses divide and conquer techniqueEE ._*aI E which divides the problem size by Co"{i$Mng position. Give the corresponding algorithmswhich divides the problem size by'

H E c. Give the problem definition "J'%,ffi-.t&e$essboard?

Explain clearly,how divide and

! f €onquer method can be applied+6".S1ve a 4 ctive chess board problem. (06 Marks)do }q

' 'n'{{'"*,il ry, .."

sa Uetectr

fr A and analyse for time complexity -fl&,_

l (08 Marks)

Ee i;o! r

S E 3 a. What is job sequencing*ffi headline problem? FinMqlution generated by job sequencing

; € problem with deadlinq$ff 7 jobs given profits 3, 5,q5.W 18, 1, 6, 30 and deadlines 1,3, 4,€ E 3,2, 1,2 respectives.: (06 Marks).} d "="'l'itq,r? o'E s b. Define minim t spanning tree. Give high level descrifidn of Prim's algorithm to find

e E minimum spairding tree and find minimum spanning tree fof"graph shown in Fig.Q3(b)a E_ minimum spanning tree and find minimum spanning tree fof ,gsQph shown in Fig.Q3(b)

E S using Pri'nthhgorithm. a:"',,.""'-.'..."''"''- (08 Marks)Ct:a E "\ a___l_51HE 3l \ lrsE rt \ t- !*E eL-*+>,= \ffi/gq. \ f6E "r\^./a!+9 ;ts>xoq)\F6q)-VE(.) -

6 F Fie.e3(b)jrt .l

$,..i c. What is a knapsack problem? Obtain solution for the knapsack problem using greedy ''.,

t method forn:3,capacitym:20 values 25,24,15 andweights 18, 15, l0respectively.Z (06 Marks)

E 4 a. What is dynamic programming? Explain how would you solve all pair shortest paths,E problem using dlmamic programming. (06 Marks)

, ,a',$.

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b. Give the necessary recuffence relation used to solve 0/1 knapsack problem using dynamicprogramming. Apply it to solve the following instance and show the results i: 4, m : 5

values 12,10,20,15 andweightsare2,l,3,zrespectively. (08Marks)

.,,,fu, c. Solve the following TSP which is represented as a graph shown in Fig.Q4(c) using dyn?mffi-'

'#:t,*, ."

,to*amming' 6llo___,ar

(06 w{kB)

=jl -L/ \ I ,' 'i'

.rt"L-\ 64)b y*..-,uD:^ t-ti / ^\

\....s ,ji:..- & tuf ..PART_ B ! d*-5 a. Explain thtffigrling of depth-first search algorithm for the gra@ffiwn in Fig.Q5(a).'*::",,:::" k.*\i.#ai,, ffi''l4," \Y:

^.: re"':,.,f=,- Fig.Q5(a)=,'' (06 Marks)

b. With pseudocode, explain ffisthe searchireS=ftr a pattern BARBER in the given textnr n

^DnnD{clrffi\Tr :^ -^&hatg.^^) --^:-- Tr^-^-^^lr- ^l^^-:+l^ /^orf,^-r,-\JIM_S AW_ME_IN_B ARB E R:Sm

. :"d_SAW_ME_IN_BARBER:SJry{ is pqt&ffined using Horspool' s algorithm. (08 Marks)

c. With a suitable example, explain tddiild,etiHf sorting. (06 Marks)

6 a. What is a decision tree? Give a h tree.for three element selection sort for arrangingthree items in ascending order its as ic behavior. (06 Marks)

b. What are NP-complete pro.p$urd and NP-hard fuo$lems? Apply four iterations of Newton's

method to compute "tr@{b;timate the absolutetnffiative errors of the computations..q "i (o8Marks)

e proffirs and NP-hard

2 stimate the absol

#c. What do you me?q ffi*., bound algorithm? What ur. {lh*4rantages of finding the lower

bound and give..ffirent methods of obtaining the lower bor4fl (06 Marks)?.;.;:

7 a. With neqeffi?ry state space diagram, explain the solving of\ffi-queen's problem byL^^1,+*^X{-d*'}. q-*e.' k /tA turd-r.6\

a-&- E:'

backtra&ftiE.i{la "i

4-,* (10 Marks)

opfimd solution usingb. nor iire given nxn cost matrix C for a job assignment problem find offma[ solution usingand bound method. Give complete state-space tree for the instarlcg- assignment

,,;:*.poblem solved with best first branch and bound algorithm. '. ;\' .,,*F-i jobl job2 job3 job4 \"r/

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8 a. Explain different types of computational models. (10 Marks)

b. Forgiveninput5, 12,8,6,3,g, 1!, 12, 1,5,6,7,10,4,3,5 totheprefixcomputationproblem and O stands for addition, solve problem using work optimal algorithm. (10 Marks)

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Time: 3 hrs. Max. Marks:100Note: Answer FIVE full questions, selecting

atleast TWO questions from each part.. PART_A {;,i*'| , ,,, Draw the connection between processor and memory and mention the functiona,of each

, Qomponent in the connection. i,* , "(Ot Marks)

b. pite the difference between RISC and CISC processors. . ^;...,'

'. (04 Marks)

c. A progra* contain 1000 instructions. Out of that 25o/o instructions reqffip 4 clock cycles,

40%;'.,{ns"}ructions requires 5 clock cycles and remaining requirqq*3'clock cycles forexecutiti$, Find the total time required to execute the program rug,q,flin a L GHz machine.

""' ..:' ,;." . u*,, -r, (05 Marks)

d. Add +5 and -9 using 2's compliment method. r t'r' ,r,,, (03 Marks)t '1"'..t...""

2 a. Explain immediatei'lrldirect and indexed addressing moddb.', i (08 Marks)b. Explain different rotat$ instructions. :.,,:,:,,,,

'r (06 Marks)

c. Write ALP program tq copy 'N' numbers from:*rray 'A' to array 'B' using indirectaddresses. (Assume A an&'p'are the starting mepg,,ur{ location of a array). (06 Marks)

*0.

3 a. Explain the following terms : " n

i) Intemrpt service routine ii) ir{te6pt latemy iii) intemrpt disabling. (06 Marks)

b. With a diagram, explain daisy chairlurgltqchnique. (06 Marks)

c. What you mean by bus arbitration? Br.fufry'explain different bus arbitration techniques. _

5a.b.

c.

6a.

With a block diagram, explain how the printe;:iS hterfaced to processor. (08 Marks)

Explain the architecture aq,d.,,f, essing scheme d$USB. (08 Marks)

Define two types of SCSf c-ontroller. (04 Marks)

'':'rl'--: " PART - B ""'"""''

*'J*, "Explain direct pbrhory mapping technique. -'k--_ (06 Marks)

What is vrrtua-'t memory? With a diagranr, explain how virtua, **.,ry.1ddress - [t"ili:if'

Exptrqid6hs working of 16 megabyte DRAM chip configured as 1 M >o'16, mory chip.

,, ,,i i (06 Marks)

,D iSn 4bit cany look ahead logic and explain how it is faster them 4 bit ripplqadder.. (08 Marks)

Multiply 14 x - 8 using Booth's algorithm. ' (06Marks)Explain normalization, excess - exponent and special values with respect to IEEE float"irgpoint representation. (06l\,Fai'k

7a.b.

c.

8a.b.c.

With a diagram, explain typical single bus processor data path.

Explain with neat diagram, the basic organization if a microprogrammed control unit.

Differentials hardwired and microprogrammed control unit.

Define and discuss Amdahl's law.With a diagram, explain a shared memory multiprocessor architecture.What is hardware multithreading? Explain different approaches in hardware multithreading.

(06 Marks)

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