This document contains the questions from an engineering mathematics exam for the third semester B.E. degree. It includes 10 multiple choice questions covering topics like Fourier series, Fourier transforms, differential equations, and linear programming. It also contains longer questions on topics like heat transfer, interpolation, eigenvectors, Poisson's equation, and Z-transforms. The exam tests knowledge of concepts and computational skills in engineering mathematics.

1. 4'1s"- rs
IOMAT]1
Ttird Semestcr B.E. Dcgree Eaniiirltigl; D ec.20 I .r/J. n.2 0l s
Engineering Mathematics - lll
Nole: Ans'w a,! FIVE .lt qattions, seldihg
al.ast 7 WO questio": fro eoch rart.
a
E'
2..
,a
itr
aa
t"'
?,
.l
-1
Exraid f(x) = Jl-cosx,
til
Fnrd the hall+anse sine s$les or rl )
t0 150 t30I I0 tro
r7 0il02lnc 251.17
FiDd the consa.r rerm and the tiij tso harfronrs in Fourier serics cxpln$on ofy
Find Founer tunslorm ol e
b riLid Fotriier.nr trrnrum
c Sollc nre ifiegraleqtration
Fi,rd Hrious possible solution ol one-dineEional heat eqnatioD by scparable varnble
mcnrod. oo!{rat
A rcchngular plare rilh insulared surfacc is locm Nide and so long conprcd to ns s idrh
drd n nny be considered nriuite in lensth wnhout i.toducin-g an appreciable eror. lfthc
letupeuxtreoftheshorcdgey=0ngilenby
'r,,.,=lrl
lo.
1l+i
: r0 (r0 x),5 <a ! L0
.nd the lwo loig edges x= 0. x = i0 as $.ll !s rhe orher shon
f-it acune ofrhe lorm y = aeh' ro the data:
L]
v rslrl
edle aE kept at 0'C. Fnxl rhe
ll0Nlrrkt
Usc emphicxl method to solle
,lininize Z=20x -10l
:L - 2rr >:01
3xL - 2x: > lll

2. 0. Solle the follo{ i.g LPP by nsine simp lex nerhod:
Maximize Z= rx' +2xr+5i. -
Subjed o rr + 2x: + xr <.110
3xr + 2xj < 460
x + 4xr <420
x >0.x.>0
IOMAT:]I
(0,lt,io
(4.99) by using Ncwron s
(07 rtu.k,
() bJ using $vron' divrd!d drrlennrc
Find 40.1) by usns Ne{toi s foNard inre@olation fonnnla and
backl,ard interpolari.n romud ironr thc data:
1 1 l
[.] -8 0120 :0 212
liind thc i.re.p.h.ns polvnomral
0 -l 5
flr) 5!Ill8
usinE Weddlc rule Takni r crtu.l $b nrena s,
0 id the tu llo$ ing sqmre mesh. C!tr} our two itaations (07 rhrrs)
PART - B
Use the Causs-Seidal ite.ative melhod to solve tho syslem drl,ncarc.tulions.
2?r + 6y-z= 85i 6x+l5y+22=72i x+y+5.tz=It0 Crry our iieElo sbyrakins
lhe hnial approximarion to the soluton as (2, 3, 2). Consid.r aour deimalplac* ar tuch
stage for each la.iable. (07 Nrrrk,
Usi.s the Newton'Raphson nelnod.6nd thereal rool olrie equatioo xsnr - cosr:0 nelr
ro = i. cariyout lbur ireBriois ( in radians). (06rr,rk,
Find rhe largest eisei value and thc corespondins eigen vecrorolihe nmti
/4 r-l /r
ltA I . Ll b, nuer nerlod. Tar, 0|a..- ." ecro-. Pclonn 5 _reEr.vns.
| 2 )' t0
Son€ rhe Poissor equaiion
boubddy and mcsh lengrh. h
ibr thc sqDare meslr Bilen bclow Nirh u= oon ttre
(06rark,=l

3. tj rn3 a. Findrbez r"nsfo'dsof i, iil l.os
l:,r
j,r
b. Shre and prove initial value theoen in Z-tiaBfonns.
c. Solv€ lne difierence equation
u... -2!,-, +u. =2'a !o =2,u =1.
E,€ruate the pivotar mru* or
*=16#
condiionsare u(0, tl = o, u(5,0 = o. 4(x,o)
lOMAT3I

4. USN t0cs33
,,2
1":
ia
2z
a1
..
a.
::
a=
;
E
Logic Design
iote: Ans||q FIyEf l qaesnas, selactina
at leasl TWO quesiio"sfro,n each part.
using only univeisal Sates
(05Ir,rk,
equiralences in positiye and negative
(0sIr,rk,
An asynmetical sisnal waverom 6 h,sh lor 2 n sec and low for 3 m sec tind
)rrLtuen() tr) Peirod
uhat aEnniveBol gates? Realize
Discu$ the positive and negaiire
d ExFlain thc srucue ofVHDL/ Verilo-! progEn.
a. Cive statelransniondiagramof SR, D..JKandTFlip Flop
b witb a neat losic dia-sram rnd riurh rnblc. explain the uorkinS
Flip Flop along{ith ns impleme.tarion uins NArDfates.
c Showhowa D Flip Flop can beconle ed inro JK Flit - Flop.
The syiem has four irputs, the output f illbe high o.ly sne. the majoriiyolthe inpuh are
high Find the followin8
i) Ci!3 dre trulh tble and simplilybrusing K-nat
ii) Booha. expEsioi in Irn and IIM fonn
iii) Implemcft dr sinplified eqdation usihgNAND NANDgaresa.dNOR NORgates
00 Mrrr,
Find essentidl pinrc rmpli@ts 6r the Boolean exprcsion by uslne Quinc Mc Clusky
iA. B. C. D) =: n(1.3.6. 7.9. 10. 12. 13. l4- l5).
lmplenentthe Boolean tunc.ionexpEsed by SOP l
AB.,.D -I,,, 'i.uo..? ,....s8 tu tv..
Ihplehentatulladdernsingxl-r.-3decoder.
Deisn 7 sesmenls dccodci usine PLA.
IASL]B
and tinring diagram. cralaln rhe wo[ing of a 4-bit SISO rceislcr.
codeforswitched laiI counteiusina asisn"md alw.yJ statene.r
a.Designsynchronousnard,5UPcouoterusingJ(llip-Flop. (l0Mk,
b Explain a i bil bimry RiFple dosr counter, give the block diacmm. trth ftblc and ourprr
srvefoms. (t0iu,rto
l.l?
(A+B).(

5. r/?.
10cs33i1(':,s"
*,,r, ;;tr.{k#/.*rin vearay and M@.e mder
D.rjgh afi.byicl'oious s.quc"tial logic cncuil for state traNnion diagEn
Iis. Q7 (b).-
ol
lo
llo0
o
Fis. Q7 (6)
?r
a. !xplaii te R,zR !addr technique oaD/A coo!6ion.
b. E&lain with neal diasrab, sinsL slop€ ,D conwrtes.
(o,
,'
-o'
?o^
")'

6. lsN
r Explain hos @nsistorcan
b Detemi.e the rxlueofrhc
R -5LO.Rr=IkO,p=
.2
:::{Q{
r'-?)
i*-; r".
//i
H(
).
10cs32
Third Sem.stcr B.E. Dcgrcc 014/,1rn.2015
circu-it-s
tar. Marks 100
)otet l. Ahs*et FIVE ful qr6tioh!, ftlalihg
at teasl Two q@stinks fion each ?at
2.Ant ntisn R tela ar be asstue.l stileb.
i
i1
j-a
:1
!-_
11,
a!
i
rs(1o6 RE and R. for rhe
(05 rtrarh,
cncutshosnin Fig Ql (b) given (har
=2 nrA lor dre silicon nude rmnsisror
(03 ND n
Es Q1 (b)
c Brienydiscu$1he $orkin!oDer ion olsilicotrconlrclledrcciicr.
2 a Explain wilhnear sketle s the opera I ion ald c|afubnsrics olN{hdnelDE MOSFET.
(03:lnrk,
b. calcllare the v 0e of operaling poinl lir thc circnn stoNn in Fig Ql 0l givm rhrl
rhftsholdvohasefor re MOSFET h2V.nd I'ro:r=6 inAlorVLlorr= 5 V. (0?Ni,rk9
Iis Q2 (bl
rilc the adLdrnges ofMOSFET orerJFET
tsieny dhcns wllh iecesary diagflms the rvorking opemlon. .ham.lennlcs and
prmmdtets oflightEnnti'g Diode o0rirls)
A phoro diode has r noise curent ol I lA Esponsivny fisurc ofo.s A,w DetemiDe irs
N.ise Eqrivaldnt PdRer(^"EP) xnd DetecLvnl (D) (05hrk,
Bn.ily explain tire wo.king operarion olopo couple^. (05 rhrl,

7. hybnd paDnere8 lor tne
c what aE the dldrages
circuil ofthe tansnror in alirhree
tansislor e h. = 1.5 kO. hr
ol cNcade amplillefi on ole.all
r0cs32
los liequenq' Esponse oa$e
(16NrBrB)
.onliguralions
-qiven
lrr rho
= 150. h( = I !lO r .Dd
(r0[u,*,
liequctrcy r.spoise of lhe
(0{ lkrk,
/tr1'.'crr"- S
le.'"".;:,' )ts)
._ ,1 '
E.F r i'lner+ad nr$
PART B
a. A poyer xnplilier in clas B opemrio. pmides a 20 v pcak otrQdr signal ro It O load dre
s,vstm opedes on i powersuDplyof25 V. Detennine lhc enicien.y ofthe mpliner
(03Yr'{,
The rolal hamonic distation olan rnplifid reduces Eom l0% to l% on inr.dndioi ol
l0%nesdivefccdbnck.DereminetheopenlootaidclosedloopsainilLrcs (06!r{t
Explain lhe dva,lases olnegatire feedback in amplilie^. (06v.rrt
caprciloN and couplinE on lhc
what are sinusoidal oscitlatos? Explainrhe Barkhausen {ilerion lorr6laif,ed or.illahons
(mr,nt,
Wid a icar cn.un diagr@. crplar. rh. pnnciple olof allon olBtrtltred RC nhac shili
os.illaror 0sNt!rk,
DiscusbrietlytheroI(ineopmriorolAsbbLeMunivibratorusinglC555tiiner (0?Nhrk,
Explaii with near diagmn and ielevml wareroms, the pdnciple olonerarion olnnefiDs
reEul.lor
Thc rcgulared po$ersupply prolides r npple rqcction ol 30 db. Illhe ipple rchaEc tn rhe
lnregulated hpur is 2v,calculare rheourpuiripple (06Nhir,
Expl n dE inponanr lcatures md parandeN ofswitchcd mode po$ersurplies (SNtpS).
(06rrrrk)
a Lhdare a ile lillers usng op-anpl ExFlain fiEl orderlos pas and hignpa$
b. Explain wilh cncun th. L(*ingope8tion olinrnLhentdior ampllfier.
c Calcularetne values olRL, Rr. C, Cr xnd Rr llihe fiherlad acuroll'
Q lactor of0.707 xnd mpur inpedence not les rho l0 (A bi rhe
second oder low pas nherbuilt amund a single opeBronal.mplifier.
I
IiE.QB(O

8. t0cs34
:.
i,:
l1
a!
Esrablish the folloqing aigufrd.l by the
-(q ^,
Negateardsimpllfyeacholthefollowin* :
i) rr, tp(x) wq(x)l
ii) vr, [p(x)^ -q(x)]
l!) :x. tb(x) v q(x)) + ()l (06 M,rrt,
Fi'd whctier the followlng argudeDl is lalid No engineerine $ude.r.ftur and second
+i]-tilill-
Third Sem€ster B.E.
Discrete
-l
Degree trramination, Dec.20l4lJan.2Ol5
Maihemaiical Struciures
lote. Answq FIVE fu4 qaesttums, sel..tins
aleasr TWO .t"zstions fmh each Da .
S,nph r...0,*prc..r1lF b,lJ B;{i ' .Jrrdnr
i) Use menbership tabLe ro e$ablish rhe sel equalily ol:
,, If A = lL. 2, l. 4, 5. 6. 7|, determine
elenrcnts. subseh of A conrxinlrg l, 2.
'lhe sample spa.e ora. expe.ir.nt rs S = la, b,
erelr B = ia, c. c, gl, detennine P,{A). r(B),
i) lp
^(pJq)l-
q
ii) lp +q)^(q + rl+ (p +,
Snnplity lhe swichnrs network usins tbe laws oflogic.
(07 Nr&rk,
the nunbr ol subsets ol A conraining i
md subsels ol A w h even nDmber ol
c. d. e, t s, hl. Ir e!€nt A = la, b, cl and
r)(AnB). Pi(AUB), Pi(A), Pr(MB) and
(07M,rk,
=(*^B)",i^.,.(rnerurrnc)
ris. Q2(b)
nrethods olprcof by coDtEdicrion.
6i!c i)a dtrect proolii) an indncci pooland iii) proofby co.rmdiction
stalemc 1fm is aD evcn inteer, rhen m- 7 n odd".
l oll
A.il is an enEiDeering stude who
,'. ADil h noi in se..ndseme{er

9. l0cs34
lfH = l, Hr= 1+1 +,---,, H"= l+1+
:H j = (n +r)Hn -n
For alln e z prove rhar I
+ lm are har6oni. Nmbers
U B,)= (ANB )U
I r2 r=2+rn lri+
i) lfAr, A,, - ' .A,qU,$enplorerhatl
AL^A?^
^A!=A!Alu---'-uAnii) IrA, BL. Br. - - - - -, B" q U rhen provo thar A rl (B Ll B: U-
(A n B1) U - - ' - U (A n B^)
5 a. Find rhe nufrber olBays oldislributing 6 obje.rs amoig,l dentical contline^ rnn some
con6iners posiblyemply. {06 nrrk!)
b. (i) Prcvethar rhetunction f: R x R;Rdennedby(a, b) = [a + bl is commurarile bur Doi
(ii)Prove
'hat
if30 dictionaries in u libmry contains a toral o161.327 pages. tn.n arlca$ one
olthe didioffiy musl have aneast 20,15 pages. (07 irtrrk:)
c. Lel r: R+ Rbedefinedby
flr-5 torr>l'
-lr+l f.r-0
thd dertrd; f (-t). r rO). f (6). rr( 5.r. (07rrrkt
a. Cnea s.t Asith A =nsnd a rclalron R on A,let M denore Ihe rclation matix lbrRthen
prole rh
ir R isammeric ifandon'ilM=M
(16 4r,rl,
on A dcnrcd byx Rh iln dllides b
aid (r. l,
ii) R istrunsirile irandonlyil NIM: Mr<M
Lst A= 11,2,1,4,6,3.l2l and R be the panial order g
i) Draw dre Ha$e diagratu ofrhc Poset (A, R)
iil Detemihe ihc relaiion mtrnforR
iii) Topolosically soitrhe Poset (A. R)
ler A = 11, 2, 1.4. 5I ; 11,2, 1.,4.51, and deline
i Veriry that R is an equilalence rclation on A
ii) D.temin. the eqrivalence classes t(1,l)1, t(1.4)l
iii) Detemine the par&ion ofA indu.ed by R.

10. l0cs34
Define cyclic gronp and prove lhai erery subgroup of a cyclic
Deline the codins tunctio. E:21+zt by meatu
'=[.rr+rzsJ
, fr z:rsr'lP
la2i,tr5.J
Detmine dB. &r. 81, (0l]Ir.
group iscyclic. (07 Mrr,
ol parny - cneck mtln
l0
']l; I ; I :1..,..,.*,...,,......,..
, o o ,]
i)
i,
')iD
: zf + zi be ad encodins tuncrion Bilen by a gensalor natrix C
, rq k md'' H rhen poe rld c L LzilbaEr prcde.
it, .r I
r" A-{1. lr.b.ccTfbe rr'c rdbFe, o. he nnc R M-/).hen
Ltb ct
Prove that z. is a neld ifand only if6 is a prime
Prcve dff in zB [a] is a ult il and only ifscd(a, .) = l.

11. :q:s,
'. lrtion. Dac.Z014lJ
with c
t0csl5
Third Semester B.E. Degree Examin
Data Structures
tus
1
2
i..L
ia
-!-
a=
7'
?:"
PART A
a 'hat oE po i nt$ variablc s'l Horrodeclare a poinrer vlnablel (05}lart,
b wMt a,s the laious memoD allocario. techniquesl Evlain hoiv dynanic aLlocation is
doN usins nrxlloc( )r (t0turrL,
c. Lh.t is recn6ionrvhar are the arioust).oes ofrccn^ion? (5!,*,
a. D.tine stnroitre and uion wnh $lrable eamnle (03y,rk,
b .re a C pnsnm sili an appropiiare stuctuE deiinition and r&iable de.l&arion ro sroE
infom ionabour an endoyee. usins nened {ructurcs. CoDsider the followios fieldJ like
r.1 t'll.D JOr'Da..v.1' e-,, cdarLBa....DA.HRA.
D.line stack Cive the C inplcmentahon oapush xnd pop tuncliors. hclude chedk lor
enrprrand ftllcondniorsolsraok. O! terr,
b writc aD algrrithnr to convefl innr to losr li expression and apply rhe same to.onven the
Ibllosing expEssion lioin i. t ro post fix.
il ((rbLc)+(Jre)l td, !,
Nore: Ahstuet
"ht
FIVEfull ttt6tions, eL.tinA
arl.ast tWO rlkstionsftun ea.h part.
nNrt erd del.re opemrion on queuc
00lrfk.)
(10:rarL,
5
Dcfine linkcdliJr. vite a C programro lnFled.nt rhe
ErDlain rhe diJf.renr r}T)ss orlinked lisr trnh diaqrxm.
PART - B
ii) Coorplere bnrary tcc
iii) Almosr corylete bnrary tree
l. bieldescribe anv tire application oltrees
$:nar i rhre.ded birarytree, Erpl,rn risht and lefr in rhrcadcd binary rree.
w e C tuncrio. ririhe follo{insrr.ermvc(atsl
i) ioordcr li) pEo er lii)po{.der
]rplxii.lin and Dor herp sith exanDle
a L.plcmeniFibonacciheap
b. $,I!t is bi...rial hexp? Explaln rho
(l0u.rk,
sreps nrvohed ln ihe deletiotr olmnr clenenr nor a
b Epldin rlre Ed-black ree. Also, $arc irs pr.penres.

12. l0cs36
Obieci Oriented Programming with c++
z
-
,!=
!-
aal
=i
;i
:,;.2
ai
a Dcfine ftiend tuncrion? Explai.
tllustrate Nith an example.
hd n oFerator overloadingl
oerloadine the + opeEtor Aho
a vhar rc viflual tunclionsl 1at is the necd
diilcreDr form l.te bidingl
ot.t Ahs ., FtlE fqll q@stio,s' electing
aneast TWO q uesnons f,o"t each Pa*
PART A
Exphnr rhe lernB cncapNhrnrn. polmoahrm xnd niheritance rn o$Fct oriented
Drofranrming. (06 Nt'lkn
i.ni,ln rt
"
Jln .",r Nn". or u.guftnt pa$ing techni lues. r h exaturle (06vlrl,
Nr.- k n*di." .;l.dino? rne a C+ lrosranr to denne tlree orerloaded tunctions
aE( )to find dea ol rcdang-k. areaofrecr&gnl.rboxedmeadrcir'le' (03Nl'rks)
what h a connruclor? Hox is a constructor different lron nember nuctionr nst8le ivith
aD exampl€ (t6Mrrl',
wl[t ; Jtaln data membds? Explaiil wilh an exaLnple? what is lhc rse of staric data
me besl {06 vark'
Wrnc a clas rectanele conrair)ine Nro data itetns lengrh'and'breadth and fou tuncrions
* J,..r'. :e nd .,. d f .'ldJr,( r - d
"-ed r ro c..'e e e"' ro ore,.''.'o ;d.l.e'r
,n-,. ., ;.0., .'. ,o nod rl-. r. o ..( 'r,'sle re'Pe..'c '. A '1c d idi'
prc-sam rhich de.lares rlre objccs ed us.s rhe mcmber lunclionsofthe'18s' (03v'ik,
$har are rhc rules to be uedxhile using a niend llnction?
(10 I'116)
Wite a C-- prognm to add t{o conrPlex .umber bv
overlord >> and << operatos for reading and disFlavirg
(10 ir'rrkt
!,nl..i,.ctv1...( n'o!rd... roenlie..o.,,poNer.'.detred b e
' '.us iJb'l'] node. r L'1, ''P
tr e ii'.roreccd
vhdl i;hcritanae? Ertlain diferdnr qPes ofinhcriiance Explain the inhoiting nrulrrFle
base cl$ses $ilh an exahple. (lo)Irk,
PART B
a. Erplai! wnh an exanple, the orderoiinlocatior ol.o.nfldois ed de$rudors and pasDg
areumcns to base cla$ co.surcros ii multilevel n eda.cc (I0 Mrks)
b wh.r de lhe ardiguiries tlrat arise h Dlulriple inh.ritancel']Ho* to oveicome this'l laplai'
Nithexanrple. (rort,rk,
ol vinual tunciion? How is earh bindins
Hu$ ro Rn' r' rur rrhbute EplJ n ( thermpLe.
What is pure lilual lunction? v, ne a C++ Iro$d to rcate a clas called NCMBER with
an hlcecr d a oretuber and membd lnndion to sct tlre ralDe ao his dau menber Derive
thre.lasses nomthis base.lass called HEXADECIMAL. DECIMALand OCTAL lnclude
a n1ctub.r lurcrion DISPLAY( )i. alLrhese tkee dfiivcd clases to dnphy dre v.lue olbase
chsditameoberi.headecnnald.cnnalandoctalEspe.tn'elrUsetbeconc.piofpue

13. 1;
""{:,;.
a Defrne tteconceprof o{rcam pr
Wrne a C+ pmgram b aennc a class called phonebook
code, pietx and mmber and membd tunctions readdat(
daia menbm ,iom the keyboard lrd Enedara( ) Nhich
nenben. Enter the data for adeast nve phone nuf,bes and
and read the st r€d detaik and dnpla) on the screen.
Explain the fo lloving member tunctions : set( ). unset( )
rocs36
Explain in ddta,l IO srcanclas nicrarchy.
(t6nLrkt
snh data nrembcs ,ame, drea
) shich Eads rhe valu$ orthe
dGplays the lalues ofthe data
store details h binaty lile phonc
wbat is exception handlDe? Wr e a C-- prosmn to dcnonsrate (he
i'catchn
kelarcrds for nnplementing eiceplion handlin!
ExTlain rhe folloqlng wnh respect ro STL :