(a)

3,

Veri| Cayley Hamilton theorenr for the matrix A ard use it to find A-r. A = i i 1 1lL-z -4 -lJ

(b) Fird *le Fourier cosinc transfornr

xI -x.

of f,(x) =1+x2

-24

..: 1

'1 .

OR

flncrion llx; given byxs3.x 5 2a and hcnce doduce that

*?.-T

& hence find the fcrurier sine transfonn cf fr(x) =

(c) I jnrd thc rani-ol ' r lu{ l i r A , ,

1 ' l ' l

i3 €; l r, . n l , l t1 'Nor1l1xl J;01111" " l2 -3J

\

{4. , I:ind l;ourier serics lo rsl)re$entf{x) x lor (} :"

s lT_x ftrr n S

.1 ' .1,_r_+

3a q2

toeI

.L

12a

i tt.1

(c)

Fr'd Eigcn values and Eigen vccrors ot rne nrarrix A = | 1.1

; ;li -ro 4 -zl

l[J::ruTf#';-;,?i:,,::;.,,[j',:?,ffi::q ," incr,es or. "enain ,nachinc pair ror rrre rorarion x or rhe

,\ 0 tr /{t znrc ! srtt, 4r/6 5r/6

0 9.2 r4.4 l?.8 173 | r r?

.1 .

(a l

{b)

{c)

I r1't

(ej

fficn.ol:-rr

solvc: 6 '" - E'"

Solve: (D?-2DD,-t5(D,)r)z = l2xy .,ii.

Solve. .. & = cly = dzz {x+y) z {x-y} W

Find paflicular iruegral of tD-2)-t = g(er,+sin2x*x1

Using Lapface Transforms solve: d'* * "

_d)( L . -- _ _ -,dt ' - "a1, ' "*"5 ' lc= e-"

dxAE*4x+3y=

Attempt any rhree.Sotve:-(U+cq)t - 2g+cq[alcp)s + (a+cp)1Solve: (xit')pq - xylpi-qi):t :'0.

-r

solve: d:Y - y = cosxcoshxdx4

Solve in series the equarion (L*xz) !2dx2 - *ff - y = o

'6(a) Solve (3x*2)r92 +11- iu. , -std! a.--" ' r d", - : \ - r*" t ,1& -36_y=3x2+4x+l

\ l04l(h) A lighr horizontal strul AII of lerrgrh Lis tieely pinncd ,,,1 &.8 uu.i,. uncar.rhc acrion of equar and opJrsirec'ntpressive ftrrces P at eacll ol'its cnrjs and cairils a load w at its cenlre. profe tnat the deflection at the centre

is given bv +" (+,*. , '4 - * , where n2 = Pzp \n Z z: t Ef

OR

5(a) If ffy n nz o"l-1--d act

- t' ffi

repr?setrts thc vibration of a string of length I lixed 8r both ends, fird thc soluriol withI

I

boundrry c$ndir;sn$ y(0,t) * l{rr) --g,rrr6d8itlsl candirions

(b) Ij''tf -s1;i' ".f;,Ju,i1,,,. charge qt#.R#*{= Esjnv' t where

lf R? < (4LlC) arid q * 0 = i; whcn r

r . dYv t

_-:-

'd t + 2X + 5y = et

:0

J

t0el{b)

(c)

(d)

l04lby

that

()n a

j=dQdt

plate of the condenser is given

. The circuit is tuncd lo !,esonance $o

w'=JLC

show rhat q

andi=

s-tnpo ]

:$,

xmEt

RW

IEl . 1= lsJnwt

XI" I' P'/LC

[=l .g

l-costt t + s 2L (cospt +

- rq l

e "' sJ,npt..*r

where p2 = Lt / -

'ri'.:

?rr-:a ;.+.

R2-4L

,; j : ' ..

r ; . :

' i { .

' :'l{"'i,',. : : : ; r . . ,

. i . r r ' : , : l .

' r ' . . : , . :

1l i

DIIARMSINII DESAI INSTITUTE OF'T8CIINOLOGY J

lD:. D. . {tNfVERSrTrl, Nadiad.

oara,rlr--zoo5 r,B:tdff.3if$ti?1ffi rril{E: ro oo m t.ooDAY: THrln s\^'l EXTERNAL EXAM MARKS: 60Instructions:

l. Assume suitablc data if necessary.2. Write cach section in scparate answcr_book.3. Numbcr given ro rlre right indicarcs full nrark.

e.l. t)o rs ilirccrcti: -spgl-l-oii -l

] l ; init our V(S) of signalgivcn in l ig. I ." \ l l t) l

: Slatc it provc conditir:n of sl,mmciry in Alt(-l) l.!$rornr:tcr,3 A scrics l{ * c nctw.rk is connccri'ti rvirh 5v ruppl" thr.riugh a srvitch. At t *. 0s*'ilch is closcd. Dcsign nctwork such tiral ur t * i0r'"*rlrirr)rlr should chargcd upto 9ll9/o ol'its final value.4. Find V; ( 0+) for a ncnn,ork givcn ir, fig. 2.5. For a serics Rl.c nctrvork, R = 3Q, l, * | h, c = 0.5f. Iior givc' vnluss syslcm hasoverdamlxd rosponss. whsr firooifrcations n:guired ro giring criticalty damrrdtrcsponsc. I

IIQ.2

(Al.l.:l a ncl:vork givcn in fig. 3, swirch K is closcd at t = 0. Irind i , di/dr ,d ' i /dt 'ar t=0+.(i3) L)sing Laplacc rransfornration method. f r'cr i2 (t) for a ncr*..di givcn in

tsl''lig. 4.Srvirch is K closcd ar I = 0

i5l

Q.2 olt ------..--

(Ailror a nclwork offig. 5, v1 (r) * ] sin t. r > {)" v1 (1) e 0, { .* (}. l,rind v" (l).

(ll) Using Olrcrational mc&od, find out i(r) for a givcn L{uarirrl.

d:i/dt2 + di/dt- 2t r r: , i (0t = 44, di/t1r(0-) = -2Alscc.Q.3 . :(1) corvolve two signalsgiven in lig.6 u*ing grryhicsl radhod.(B) Ffud out z- paramcteisofrro:turork grwn in fiS. :.

oR ----------Q.3!l] li"d our equivalent T * nerwork of givcn nerwork in fig. 8.(B).In nctrvork of.!ig. 9,elrt=A switch is moved from positio'n a ro b.

Find out i(t1.tt'':

tsl

lsl

tsl{sl

,''ii-.ril,:1;f,.{i*,,.,*,r'

[5] ,

[5] '"

' : . . . t : .

r t ' . " i1. : i i t ' .

ffAr*'o* j '

€

Page I of4

Q:-1

, lrrrd m,ain( )

- t , ' , { chi tdobj: coul. . . : "n Inmain":}d) \\hat is 'purc' lirnral function ? l\.hv it is ncedccl ,?

e)r' \4'hat is thc ambiguiq, in mulriple inhcriiance,? Horv can you solve ir ? Explain'with sui table examrrle.

a) Assume that a bank maintains $vo kinds ot'accounts lbr custonrcrs . one caiedas savings accounl and other as current accounl. Thc sar.ings account pr.oviclcsintcrcrt rnrJ thc rvitfidrarval facilitics and no chcquc booh ticilitv.Currlntaccounl holders sho:rld also mainlain a minimum balancc ancl if the balancc f,rilsbclow tlris lcvcl, a ccrviuc clrargc is ilrrpolcd.

crcars a class accoun( that storcs cu.stontsr namc. accountnuntbcr. and trpc o1'account. l )sr ivc thc class s;rv- i rcc and cul_ucc k.r lnakt. t l rcrrrr t t0rc spcci f ic to thcir rcquirct t tcnts. Includc ncccssi l l nrcrrrhcr l rrrrc l i r rrrs i rrol . i lcr lcr aclr :e r c l l rc lo l lurvi l rg l : rsf .s l l l

I1. \ecc1;t r lc l lu.s i r I r run t l re cusr()nl{rr arrd u;r t l ; r tu t Ic l r . r l : r r rer ,l )Chcch for l l tc l t t inr t t t tnt l , ; i l :urcc. i r r rpose pcn;r l l r i l l rcr i .ss:r l - r . r r r r l

u l ldatc t l rc b;r lanccl ) I )rsp h i t l r r : bl l l r rc cJ) l 'ernr: t rvr lhdlarv:r l alrd upt l . r tc tral ;urr .c5t t.lsc thc conriructors lirr ;rll the cllsscs.

h) l . rplarn t l re cnrrccpt cl"ornrainsr: l r ip ' witrr suj talr lc crrrnptc. I . i l

{ )tt

{ . f .1 ; r ) ' l ) l l i | |u, twlr g lJrrs '1 lo s lurr . . lurrr l lq. ; .s11;3r i t t { 'u1. ,*rr , r r r r l l , : r f r rc l r l r t . i l le r f r : r l i r .c l r'.\ t:tc it r)rrllp itnt tlr tlo tlrs lirl lorr rll l l trlx.L.

' ; t ) ' ' : c l . l { l t } {11): t r l r r rc c i rs . l , l t . . { ' f

( .c ls i r r : . l ; rsrl ' l i l l l . l l l tetc . l ts lhe ol l lcc lof ( 'c ls i r rs i l r rssirrr r l l l r r r l r . , , l , . ;L. . l i r l

l ia l t rct t l tc t t c lass. \ \ ' t ' r tc col)r 'srs ion r<lut i r tc i r r sourcc c l ;ss IAtI t ) \ \ ' r i lc i pro$alr to <lef inc conrJr lcr c lass { rv i th rual and inrapin;rr-r , ls i { 's thr:rr t ;ct t t l le lr ) anr i {r ' o lr : r ! r lat l '+ ()J)fr : r l { )r lu 1>eriorrrr lnul t i l l l ic i l ion ol l r lp, ornl) lc\ r runrhe ls.

lJ I

r ) I

: i t . / - I l ( ) \ -_ l l

I )rr .rs . ltr tt lctl.. r t l i r r r l , r t r l Cf" l ' { r t \ r1 t l lc l6116r\ I ! , . , } i1. : : r . ' l . ;g l \ .

I ) l i t roul ,opclr l l i lc : ios. i r r l { )s, , ( )ut J , ( rs. : i t lc } ,: ) i r r f i lc .operr l r rgcl ;

h) \ \1r ; r t : t rc l l rc;r t l r . . r r r l : rges' l s;r r . i r rg d:r l ; r Lt b i r r : r r r l ,nn. /c) Lrplain the diflcrcrrcc in opcration bctween thcsc rw,o $tarcmc:lrs,

pc$on pl{ p2);

, Persol pl ' 'p?. where pcrson is a ctasr and pl.p2 rrc chjects.d) \[|}ra|doci lhis poinrer point too ' :'

l . t i

f2lt2l

{ t l

ls,

i } l \ ' r . i terstatgmenlthatmovesthcgel .pcrr : t ter . l .1h11eslrae} 'wardt i .omthccurrenl position '"''loi-'*'h1cur-calletl

ft' lllt ' i ;;;;,,J crr:rs 'it ':rtt\ ' :ttttl torr*t lltcrn'

\ lrrn{ }I r l t t l +1r. r ' i t 'u ' r

p"s. s-p: I.*l l tt l-

l;'ilili: 1": :H1';:1"' "t r ncn<t. c rass wi trr sur tabro c xanrp r e

:i YJtr:;lntlx l,lll-li::J"'T;:tiJ l'T"Jlon" or thc trrc is

'asscd.s,,, iil,f,"jf,$il'ii::lll'"'u"'o'1 r1":i,1]';,lcrboar d antr slorc trtc nunrrct ttt't

lile ( 'l 'tlRlf'rlali' ilr'thc no is tlivisiblc trv 3'

.t ni*.u.* rhc d;lfercni mntt** to opcn a fil-' '

; r ) \ \ntcaproSram|hatstcrcst l rcdatao{.5studtnts inr l rc|r l t ' .s tudcnt.(3l . ,an{ lrhcn displa),* il; ;il"ni"n or .rr ,rr" ,t a.no whosc p{fccnlagt is E r rttcr

Itr 'rrr 'x) ;rrxl ;tp;titt r l isi l l :rvs tlr:rt l lx' - ' ;t;; l ;:;tt lsl:tttr l i tr lt

t-rNn;it lct cl:rr"

" l t l r l { r l l l r r l r r ' l t \ { t l l l ' l r l l ' r l l r l r r t l l l ' l l t r " t

' " ' t " t t '

" ' l l l l r " l r { l r r ' l r l ' l f ' l 1 ' t

1,1\ \ n l t . t l t r { r l ' r ' t t " " ; t t ; " t i ; "1\ \

t rYt ' r l l l t ' ' l r t l l " r \ r r r l '

q l ' r i { ' l r t . l l \

- * : t t

"

' ' *

1]" t ; l : : ""

"1n' t

c l ; tss t l t : r l r c, . , r csc' t \ t r t t r t ' t r r l t . t tn ' t t r i t r t r t t ' : t t t ' i ' '

sur,) l l ( l \ ( ; r i l in i t l tc l 'cr t )

( ) l<

. r } \ \ , t i {e 3 | ' | { ) t i | . . r r l1 . . , . . , , ' .1, . . . . ; r rx| , r l i r1l l : r1. l t t 'e l t r r l ' g. i r .err . '^ l } rr l r . lculs i 'c 'e i r . le

t'ectanslc' "iongi' ' ' i:*cl

virtrral lirrrctitn "t"t'"pt' i 'sc"slta|e :$ lrlrrc cl;rss

l , ' t \ \ ' r i tc;r progr:1m "" '" t i t

1 i .c anr l tu"""r" ' t ' * i*nr" ' t ' t l r t i l l \ l i r lc lo l l tc

' *.,,tl i fitc t'ur il l rcrctsr rtttlct

\

l r r

r i ll . I

t ( ll - |

'lF.

1:::t i'

u L -+- l r-- -J4=_DHARMSINH DESAI INSTITUIE ON ISEIII{OLOGY, NADIAD.

",. , IDEEMED UNTVERSITYIB.E. SEM.- IrI [EC/CX' tlclcwcL/rT] ExaMS

December 2' ?fi82Instructions :

MATHEMATICS-III

l .JTD.

Answer each sedion in seParseparate answerbook.

2. trigures to the right indicate m'aximum marks for that

SECTION I

2sSeat No.:--

Time:l0.fi)to 1.00Max. Marks: 60

. i

I l2 ll .(a) Find Fourier Series ibr i(x)

ett

l : ind cosine sci;cs 1'or l(x)

= x2 in (-r.r)

- e-u*- e-" t

: x-x ' in (0.1).

221- r" 2 l2 -11

Prove that in r0.r) 91 z I sinx 2sin2xn I a2+: a?nA

* 3sjn3x . . . . . |a2+9 I(h)

' {e )

i r " o r l(d) i l 'A : lz - -11 t inct n 3-3Ar-A+ 101.

i.r -r. 1 J

{-r

LZ(t)

(c) I;ind Fou.ier trurslbrrn of 1{x) =gi*^,a(x(b

=0,x(a,X)b

is orthtgonal.

= 1-x2 i f lx l=0if lx l >

,,lt'' ! .:"

dx ry".:

' ' . .

proverhatA o t

l0el)

{r) * Kxfor0 3 x s l /2= k(l-x) lbr l/2 5 x { I

lr' ," t' n'1lZ, Z, n, u" l

l t 'u ' " u ' llaz Sz 62 72)

( l ' ) Irind thc riitik vl tlrc riiatrix A

Otrurlu r Crxinc ecrlc* ftrr F{x)

lbst for consisteacY & solvc:3x+3y*22=l,x+Zy=410v*32=2,2x-3y-z=5Find Fourier transform of {1x)

(cj

J-

(a)

(b)

fI

, - . r l 1bvaluatc: L -i---

I s2 (s2 - a2)

II tri, methul r,f residues.I

loel

<lI'r l.

: .,.

ii.i

Ii

-, , i. r ' Iuse rt to evaluate: i 'rf

,t0

(xcosx-sinx)2Ax'

(c) Find Fourier serieg for f(x) = xcosx in (-n,ur)'

. . : ' . . r ' . * - F,

ffi4*Xl*.*

. : . t_,

l

i . , 't .i 'iir-sfadF.$

6lt r l2J

3.

(a)

(b){c)

fs roFird cisfs n*"ue * cigen vectore for the matrix A = lo t

I

Fird Fru,,,.r series for ,f"l : *.. in 1-o,o; LO 0

Find Fq:rier series for f(x) : x2 in (0,r)

- _xr in (_1,0)

SECTION.II

i1r .Srr lvc

-

*) ,=0l.< "

_I

Srr l ,c . - : * r?D * ] ) , = 7 uVt- 5

sutvc: { [ ] -5D+4)v _- 3-2xForm tl,'L panial difi'cruntial cquation fion l(x?-y?, z*xy) = 0.Solvc: Z ' ig ' '+ql +l) = ar-

Solvr : dz * _F:t_ * 6t _, = t \ixz dx)y dy

Solvc: tDz - 2D +

x-)olvc: secy ++oxdy

Sofvc: zg , _dy.dr At

dx dvi , d l

4) y = e 's in{

4.,=cosx,+[* , r ]oy2

-2x-2y=5e'

4.

(a)

(h)

(c)

(d)(c)

(0

\

5.

{a)

(b)

(c)

= 3tany , z{x,A) = j {

6.

{a)

(t')

(c)

=4X+2y+5o"t

$ofve; y.1 !2. - , r*- + Zxy = 2x:s in(Jogx)dx2 dx

SOlvc:p+q=sinx*siny

"Sotve: *-k=s!.wccos2y :0v2 dxdY. :r . , , . , i i , i .

OR ' , I

- 'Solvc: p? + q2 -Zox-Zqy + I =0.

.; lgTtv *r*rcn"d-striogirio . -a

points x = 0 & * =l is inrially in a position*, 9,"3.bV Y = yo sinr(z-xfi. ff it is'ietcffied from rest this pmidcn,

'., -

"'nm the displacement y(x,t). -.

==:=:*****=====. . , , : . ,

toeJ

6(a)(b)

DllanMsr$g DEsA.r rNsrrru11E oF ,r,nr.n^*^____- rrodH*tT#il"roc:, NADr.rD.

b,teenc,aay obia^+ :;ffiffi$"*fii',iil ;?;

r.1jffi :"]=,est

orient"o n""n""ir"? and Desisn

fttl*"ator,", - !4exisum Marke: 5o

, r ' A 's '*er each sect ion in aepa.rate ,h!r- ,^_ L -

seat No. -

: ' rJ.9rt l res to the

- . ._**- . '

oepar&te ansWer boo' -c. Ma,.e suitable

-::_?n.. t"*Iil",i

an'wer book.

crearry. assurq>tio;-;;;l*imurn narkg forve r ne ce s;; : ; ii..ITffj "1L..

e. l {") srate sEcrroN - r

( l ) l {u larO; ' i r r ' : ' /J : 'a l r :c ' co ' r e

t ::) ;; :lj ;]j,l' " r' ".."',,"

"ii,li.l.:i]:".1",i::,:, qtatement .r .o J iu*o'd in u

" . r" j \ ,(3) i lH: : i

i r t ' ( -1 . ' l1e11q rcceiv( ' r is dIr r jxample or synchronous(4) . ; i ; ; ; ; : : l r ,s

a 'e associat

,, l; j H#: :di :;1,;, ::;il ijm:: :";:t,,:; i:,."Jil Derine ;:;..:"t'"*"n o**"ilJ";; ';;;'JJJTl;:il'

or a svstem'( . ; l ) Def i r re n, , t i rut i .n 1i .^- , . - , _ t5 l

,r, i i jr:*Activat ion (rocus or contro't I n"trich

{ ,{) Bxplajn J. l l l Toun by fork Is used ln a scquence

(s,,.;i;;; *;ffi1;:j{*ii^:i:$iil,i; ;t"ff;;v,,y dlasram0.r, , ,

* ; : ; ," i : l r l : :L;; ; " . ;st tonshiF '""4- in- iJJi l^un. dlasram.

!r ) E.rpl.i ,, . ]]i nt i i" '"..n..l '] '" ' ' i '" 'I owj ncr '

( r ) Dcscr lbe ;e 'crar iz. t iou

; ; l ; . : l#; : : . " , ,o / ,as-a relat icnshlp, I l0 l

dlagram. ot l fe.et) t tYPes (

(4) Glve the =r""^^,-"-

Lypes of rerat ionship in deployment

{a) . : ' :9" ts for f o ' r Jowing

i5) *".ir; j j :#;: i:." lb) statJ (c) Ar,5e"1ation

{d) cr.assi { fc 'ent types of $e$sages u. . : . .cJ rr , **_, ,^*-- l t ' " t '

: . ' ' : , " ) r r raw th+r , r . r : . : j ,Jr . ,^ , -

- r ! ' u *c: ln seguencc diagram.'' r \\')

:;TrJ[:;:,:::;- o''"n'"^'r;: ;ff;i:';i;jn'lijij]li."n rrom rsl

0.: {u ) Draw the c,a^r - . . . - - -

oR

rhar has l : i j : .1 ' l : " r d iasr; -Es

t,Jeb servei"l i ": : :?, 9: ' i tnl ' i : . i i , database clr iven web-site

catabaie ;.,;".'i11"3;i5i:r.y:'o.'f=512s8 os=$

^ ., , . user can e^- oatabase l^.5t" i t=it i"#ttdows

NT

v. c (D) Drew the ;: l i" : . r l . i - i .o=.loft 'u"t"=otutr."a'

oS=windo*

"1.

( iorrabor";i;";;;iiJ"i;lti#'i":ir';,liil"lrr.,''l

I

Iq l

i ts :i ' fs issqrroil,rr

Q.4( 1 ) #"fi":l;j"li :::"g. quesriona

vLrtuar run..lll"s. aoJa ;r.t"ij-" ;'-'64'rrrhar runction i "n ti,.1 -1";:"i:::jffi

i;..r;l::":, i:: .. o*."rH$l,

;:\. ''. : :'f iiof 3Page

s*!r{F-: '

l , Ii r l

Io:

a) Is i'gnoreci b) Becomes concrete

c) Relaains pl:re virtual:l - d) Is not accessible'

(2) what is tb-e tei-dt"t descrlbes the hiding of

implementadJ;;; irs ot objects from each other j-n- a

C++ cl ,ass?a) EncapsuJa'- :cn' b) Data hiding:

c) Daia i4 ierentai ion' d) Data abstract ion'

{3} Which cf ghe iJ i"" ing do you thlnk is used to seParate

the base classes in a-base class l is t?

a) colrsoar ' f l l -coi tn ( ' ) c) seml*colon{;) d} Ti lde (-)

(4) l low many fulc i :or ' cal ls are made for the statement A=B+C+D?

a)L b: : c)3 di{

(5) which u".k; t" Parameter do you thirrk js used in the seekgo

lunctron tc: pt=t ' i 'on the pcinter to the sLart of the f i le?

a) 1oS::s l : r - ' b) ios: :L- t :c l c) jo: i : : r ' ) i ) { ' I l c i ) jos: : in i t ia l

{ ( , i i r l } ren a ' lat t : ; ;ace has capa!- i ' i l ty to l l t t r r ! l : ' - r ' t r t 'w <lata ty1)t 's \

i t is sa: i l r =e

a) ove : loan*i o 'T; t* ; lated c) Abstractect ct) Exlensib ' le

{?) l jxamine the ic i lowing funcl lon protot .y l )e :

void Reaci5emo iCMemo { memo);

What i ,s t l re f t :nct ion cxpec*" ing tg be p ' r 'sscd &s al l ' argument?

a) A cHc:: lo obJcct ' b) A Cl lcmo ob]ect po' intcr

c) A cH.: : ro obiect reference d) A copy of CMerno obiect '

{8) A funct ion :

a) Can be dtf, ined insidt another funct: 'on'

b) c",t not- i*- ief lned inside another function'

c) Can not be def lned in gl 'obal space'

d) Can nct be def ined iaside class '

(9) c lass XYL{

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Q. s Find out t .ht . output or et . rors in fo i ' l t 'wirrg pl :ogram codes'

(Attq)t anv f,our' l(Assune su: i i .able head' : r f i les are incl r :dtrd ' ) t1 i l l

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++factori Product |= f8ctotr i. l whi le ( Factor == fr) ;

cout<(/ProCuei 1s "((Proclr lct<<endl ;

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t ;class der ived : pr j "vate c lass base{

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void main{) {derived d;d.show{);d.dispJ.ayO;

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publ ic :v i r tual . stat ic int f1O { cout<<' , f1O"; }{ r j ,end vir tual" int f2O { cout((r ' f2( , , , i }

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0.6 (a) [xp]s1n dl f terence bctween ear l y binding arrrJ . late bindinq . t21Q'6{b) TIF wl th Juct l f icat ion:

{1} Runt l .me decis ion maklng faciJ. l ty 'of C++ for v i r tuaLfunct lons increases t ime overhead. tz l

(?) St*t lc funcl io l r can access data members using thispolnr"er. t l l

Q'6(c) create a st . r ing c la l ;s that has pointer to c i : ; r r as data memberand - i t a l lows stol : i r rq str ing contfnt on dynarnic nemory. Over loadAssigrrment (=) o; :er ; r tor so tbal i t copi .es ccJrr t . r l t of a sLr ingrnstead of copyi : rg address o{ a str lng. t51

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*.i i-) i. i i .au r.io yol,l rsasn iry opcraLor overl.oadi.ng ancl l ist the operatorgthat you can not over l .oad. t7 l

0.6(b) t lh ich are the speci{ i .ers in C++? Explain their use wirhcxampJes. (31

Q.6(c) I r l r i le a program that. d lsplays area of d i f ferent shapes.Store di f f ,erent shapes on a s lngle array. Base claes lsshape and circ le, t i : iangle and rectangle . r re der lved fromshape.

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DgY: Tfiuesp#/ Tims lo.oo,o t. o-oInstructions: . An111te g,tifry in separarc ansr+,er_kr,oks S.fi r-Joi'Figrrrcsro--rhc ttshtdr*";il"**x *lar{rs: 60 -r Albnptall C,r"cl*"

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:]i::"rfftrilffiT.irlil:il"' ** ror rhe ne,work shown in Fig r {I0]

(b) Fino et

ln",;too"t* i(li. *'hose characrerisric equarion is.

," \JF,

o;+4i=0(c) I ' ind our l . {s;nz t} .(d) Synthesize the half wave -.hown in Fig" 2.tn

7:;#;":feralor equivalent ;Jrirkorrhe generar rwo-porl ner*"ork in rernrs orthe

Q.2 Do as direcled(A) Asq,eralor has a_voltage rariation gi"Tb

1. y guation n(,1=, "r,

r:0. This *"***,rf t0lconrpdod ro an RL series ciicuil wtre3 = o r a-*Jil,;*r* L = 0.r H ar inre t={bv ctosing a swrlch. rind

". il;;grft:

"r;;;;ilro,* orrir* (r).(B) con'orve rhe furrctions using eluphi;,r,",h;;;;;riil;,h ma:her.uticar rormura:V,(t)=1, o<1<l tu; f , i= ' i1 " ' l<t<3= 0, all other = 0, all other t

Q.zDoasdirected ---OR---

(A)Show that Lltf(t), d/r(.s) ic r*,.rr r_r.,

' {l0l

{ r}) Find AB.D * j;;H" "l';:,H#_T ::ffiJf.nn

or r cos(al )Q 3 Aflempl anv T!vo.,,t, j;;^3-^:,:::"lt *"._* i1 ris. 4, rhe capaciror c' v' u'u rru{i'('! ,- silol}'I ln l?ig' 4' the ca'aciPt. a-l i.s cirargcd t. Vo arrd dre switcrr K rs

[l 0l

*:Y*:n.i^n h"'R;=;ilh;'i'ffi00V, R, = r i\4f,r cr =ro 'F o-,r i - r.rSolveforatr*0+. I Mfi, Cr =10 FFaod C2*20;rF.

:];fffiyJffiIn:mg*ffim :'il:Tiri* 5 to wprisd b an RL nerworkrfrff: ;f t*ffi if#'ffi t i,'. : ffi #f:ii jffi F# ll fi tr?*n,{c)Apprv*';JilIffi,?i:1*#-d"#;i'ni'li;i",#TJff ;';;;HTilli*'fr1(i) T-nerw.orr (ii) II - nar+,ork

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t=r ; : , , . ,9.r Ld)

l l0l(A) A 50pF capacitor is chargod to retsin l0 mI of enerry by a constant charging currsrt of

lA. Determine the_vollpge scross &e ryior.(B) Find the expression for the mutual inii.ctsnce in Sre series corupction of trvo coupled coils,

when the flux of the two coils assisr ech other, the net equivalent inductanoe being L1 andrvhen lhe flux of the two coils oppose srch otlrr, tre equivalent induclance teing t". "

(C) Determine driving point impedanct fr,'r dle network shown in Fig.7(D) Stal,e following network function is valid or inr:alid Specify the reason(s).

Yrz(s) = 3s3- 2s + I

2s2+s+l(E) For lhe network shown in Fig. ti. Derermine Gn (o). Plot magnitude and phase of it as a

ftrnction o[ rrr f<rr o > 0. Mnke comncnt on behavior of the nelwork at differenl frgq ofinpul liorn rrragnitude plot \

Q -5 Alrernpt an1''I.wo I l0 l(A) ['or thc tnuplcd nclrvork slxr'.w in Fig.9. rvnte locp e4rralions using KVL wherc Vi11 & Vs2

arc initial vohages &cnoss capacit,.rn.(ti) I;or the neln'ork shown in Fig. 10, ryplv ioop va;iable analysis and determinc currenl i

through 3O resislor R(C) for ilrc neln,ork sholrn ir: f ig. I l,Deiffinine currsrl through l ll inductor using Nortom's

tlrsorern

Q6 t l0l(A) Detsrmine lhe powor loss in tho l0 O rcsigor using Thevanin's thoorern for Fig. | 2.(t] ) For nelwork shown in Fig. I 3, delsmrioo Gr:, Zu and Yr r.

-"oR---Q,(,

(A) If the transfornr of tho cuncnt in one port nctwork isI(s) = 5s

(s+2) (s'+ 2s +2)Dtscuss time dornain behavior from the location af poks & zeror.x. Also find its time donrainresponse i(t).(ll) The Fig. l shows four windings on a rni+inetrc flux conducling core. Using di{ferent

shagred dots estahlish potarity markings and shou, nl! the steps

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main( ){ lesl t l : daladl ;

cout' :< sizco(t 1 )"""n"{ (si zeof{dl }; }b ) Stalg l'RtI:rT:ALSW{'ith rnr$oR.

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f rplain n'ith suitahle c$rrnplc.lr 1 [,xpirin corls truclor ovcrlr-r :rti irr e w i tlr suitablc cxamplc'

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Q.4 Do as directed: tl0ll. S'hat is the total inductance looking from l-l' tenninals in fig. l0? Establish the

coils on the core with proper winding direction according to polarity marking.2. For a series RC network (output talien across C) . Find Grz 0w). What is half

power freq. for Gr:0w). Design values of R & C to have half power freq. * 1gKHz.

3. Under whal conditions rvill the reciprocity principlc apply to a network?4. Find rvhetlrer following function rcpresents drivirrg point lirnction. 1

c (a _, C*tt) L

_ ; Frcs):FrL>-' - 6c5.)

- ioo s2

ffi5. Irind dual nclrvork of circuil Givcn in fig. ! | (h1' ncglecting tlots)

Q.5 Attempt srrv fii'o: l l0 l(A)ln the nelrvork ol'fig. l2 l}e switch K is cluscd al I = 0, & stcady - state having

prcviously cxislcd. F'ind thc cuffenl in the rcsistor It using l}cvcnin's rheorern.(If) Write mesh equaliorr fer nelwork shown in fig. I I(C) Dcscibc trsnsfer function l'or the onogort & lwo - pcrt ncfworks and what is

significoncc of irnmitoncc. Find loltagc *ansfcr funclion for circuit given inf ig.13.

Q.6(A)l :s lnbl ish polar i t l .nrnrking in l ig. l , l usinglhrcc r l i l lercnt dots. l3 l(l)) What sre thc polcs nnd zeros ? What does thcv dctcrminc lbr any network? l2l(Cl) For a network givcn in fig. 15. srvilch K is at position a for a long rinrc & at F0 it

moves from position n to pcllition tr. Draw its lrans{br nenvork & wriic down loopcquations. lsl

oR ---------Q.6(A)"I'he model for M{.,S transislor anrplifier is shorvn in tig. l5 Find our Grz. l5l

(B) Detcrmine numerical valuc of i2 using sourci trsnsi'clrmation method for fig.1? l5J

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Sudect :- Obiect Oriented Programming2oot;f6 l .c1c

.A,nsw'Er each scction in separate answer book.Figures to ttre right indicarc thc marks.

and Design.},Iax.tr[uks:60Seat No.:

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SECTIOJY_I

qt: i I)o ns dircctt 'd.r) lnheritancs represents _._--.*.*_ rclalionship t,enveen classes and

rcprcsenls rclationslrip bllnccn cla.s:.cs.Irl \\hv doesn'! st.cfft( string . .p'): rvorh,lc) \\iitc a l-rsr line of a spcc rfier f<rr a class Tirs thrt is dcrivc,J ironr

and lrorn clans Rubber.d) .{ static funclion

l) should bd cnllcd when *n objccl is &xrro1.cd... ?)'can trc callcd ruing clrts nsrrc and firnction name.

3) can bc callod uring objecr and Smction namc.4) is uscd whcn a' dummv objcct ir crcard "

c) Stalc TRLIE.,T.,\LSE with rcason. l2ll) A pintcr to a basc class can point to rhe oojccu of a dcri\,Ed class.l) kr tl+'. a function call can occur cvcn on lcft-hand sids'l-an

ssslgnincnt opcfator.0 Writo down thc output for the follow{ng code segment:

class samplc { };main{ ) { sample sl: cour<.: sizco(sl):}

Q:2 Ancmpr anv.4 qucstion*: ll()la) Find oul crrors ,if aq!, gtd cone ct flpm lnd oritc ds'Tl thc oulput ,othcm.isc

simply write dsurn thc orgur.nain{ )

{ conet int j= }0; int &k = j: hcottl<<*j='<<jd{{'*n<-rta-<srdl' f,"tt -

.... :k=20: '.' r-*i jlir ' , .1o

a/ :.:

cotrl (<1'j="<<j..<"k="- .'-k. lb) Find out crrors ,ifiny,and corrcct thcm and write.Cqrot tlrc outpul.othcrw.isc

simply nnrirc Aowithd,olrtpur. :, ..,I : ,j , ,trr#*,*classbase{public:b;base( ) {cout({1irn'<*Urgd[ii h

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{ Puhlic:d2t ) :d1( ) { cout<<"\n"':{'frst": } };

main( ) { d2 obj; }c) sometimes the *"*t}u, functions are de{ined constant. lltry and how are thev

dcfincd conslanl ?d) \1'hat is the ambigurfy in multiple inheritancc ? How can you solvc it ? Explain

with suitable examPlc.,;)\\har is the cli{Icren"" b"r*"rn function orvlcading and function orrcniding ?

lixplain *.ith suitablc cxample.

a) Dcfinc fivO c.lasscs : I ) class stringdalc with anal' o1-cluraclsrs as*it's onlY dala

nrcmlrcr { c.g.. tlatc is storecl as "l}ll}v)- ) .2) chss dlte ryirh day .rnonth.l'c:r

:rs it,s rlrra r'c*rlwrs.( all arc intcg[rs.; \Vritc "

prograrfi to thc folt.rving job'

{ tr\'rite l}rc conrcrsion rouline in source olass' ) I7l

stringdatc s1: datc dl :s l* d l :

b) L,splain rhr: conr:Gpi o1 'conrairu,Tship' *ith suitrblc cxnrnplc'

OR

e:J a) Define rwo ciasscs 1) ciass circle ihat slorcs radiur'srd areaof drd circle .

?) class cvlindsr that stores heighrancl volurns of thc cylindcr '..\\'ritc :r pro$Fam lo calculalc and displey tltc volumc of thc c1'linder '( Usc inhcritancc') {51

b) Define a clnss fi.aclion which contains numcr8tot and dcnominator ts it's data

mernbcrs . \l'ntc a progrem that orcrloads + opcrstor to pr{brmaddition of

tu'o fractionr.l c'g, lii + ary1' t., t5l

SNCTNN-II

Q:4 Do gs dimcl*<l'-a) Find oul ctrors in thc foll'owing et'atancrtts''

l) il.'ilrcam.intllc{ *DATA");

2) inlilc.oPe{argc);ll/hai are thc advantagen of saving data in l'inary forrn ?

- ',",'What :s ,he .liffercnce bctwecn an[3J and j(an+3) where arr is afl afra]"

bas{ ) { cout<'fn'<<'second";} }:

: r#{: ;. : , r$

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'cunrnr position in a strcarn obji0f0allcd ft. ' .

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-/Q:5 Attempt any 4 questions:

JohnAmislr

l t0la) What is thc differcnce between cpcning a 6le with a construclor fimction and

opening a filc wi$ opsr( ) fimction ? \l'hen onc method is prcfcrred overrheother?

b) Explain the uignificance of friend function witlt suitable examplc.c) Write a program to counl urd display the length of a file which is given as

oommand line argument.d) Using pointers, write a program to copy 80 characters from string sl ta string s2c) Dscuss thc different modes to open a frlc.

Q:6 a) A filc eontains a list of tclephcnc numbcrs in thc f<rllon'irrg form.23456782528099

Write a progFam 1o read thc file and displal'thc list and also add thc dala lo thcfile. 15 j

h) \Vritc a program thal rsads a number ficm a filc I'rth,{BtlR.DAl"( n,hiclroonuins 10 intcgers.)end :tores tlrs aumbet'h thc lilc ODD.DA'I if it is r:ddothcrwi$c in thc lile [,\'Elll.DAl" . tf]

o8.

Q:6 a). Writo a program to sornpuie eid di*play sea of glvsn 2-D ob-iucts i.e.;irclc,rsctrnde, triangle. Urc r"i'tual functkxt co{rccpt. Use r}rapc as hasc class.^.. [(r] :

b) Crca& g clase rtring . ltrIritc rcquirod corstructore srd dcstruclors. Owrloid ''' *

o1rcrilor to comparc thc lcngths of nro $ringrs and displav lhc larg,ersEinS lll

ry:- 1' . . . .

r,: ':ir' I

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DHAR}ISII\IH DESAI UNN/ERSITY, NADIAD.B.E. Snu. IIr tEc/cBtrctcld.tcl,lrql EXAMS.

MATHEMATICS-M

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Scat l{o.:Time:10.00 to l-OO

Ir{ax. Marks: 60

CD^Tt^rr r

Iixprcss the matrix as a sunl tlf synrrnctric & skew-svrnfnetric nratrix where A :

Are the kr l lou, ing'ccrors l inearly clcpendenr? (3,1._4),(2,2-3) & (0.4:"1), ! l .so, f i

Stt f vc: { r : n, c. i n r -

, - ) , . -J - ' - - , - ' * . l lxdx= I 0<tr<;n

? tsI<23 \>2

f.t2]

(a)

{ i - l }

io 'n lj - to t r l1 - : 1\ l l

nd a relation bctwecn thenr

id)

{c)

ffl

Hvaluate: L'1J

, Ot method of residues.

Olttairt the fourier.serjes for tlre function f(x) = xr. -r < x ( n.

I)ct":lop sf n {ff) in half-rangc cosine eerics in rhc range 0 < * <I.

Artsmpt atry three.r:i;o the fourier sine and cosine traruform of rhe function f(x) = e' ' & hcnce show

smies in the interval I_r,ol. Deducc rhat

ia) IOelthnt

€&*g

i{j

r.li:.!

' i i{'&&$f

;ii

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iI:

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..:h: ""tr.F 'i

- :. ti". ' . . , ' i

, -1' . - t . . : . l i

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1* L * 1.1z 32 52

,.*. "'t'*iki'l

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f _cosmx r-- f xsinmxI -':--; ax = | ------'": dxuu i*x ' Jo 3,+xz

I;jt'.J lunction llx) a xsilx ils a lburier

1 - 1 1 . ! .

l'est {br coneietencv & solve: 4x-y*22*t=0; ?,*3},-zFind half-rangr .orin" series for the functiorr f(x)2t =0; 7y-42-St =0; 2x-I ly *72+ Bt = 0.= kx 0sx<)12

= k(-*) )tZ s x sLDeduce the sum of rhe series

'1: :li, :

,. .6,:.i.i,.t.,*,' t ,1,";'l*;,'

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