*${r}wg ffi - Rasayani · Discuss any tw-e:i advantage of Lagrange's method over Newton's d ivided...
10
*${r}wg hT,l - ffi fiL****r# tul Q.P. Code.: 1f8gz .. " :.1. r 2 Q.1.a) Find the extremalof f 9^ a.. J ,,'2 b) ls 10,2,-+; a linear combination of v, = \t,2,2), v, = (3.4,6) : [r 2 3) '' ' '' tt c) Check whether , = i, I + i is derogatory or not. d) Evaluate | ,' ,!, , along the parabola * = J.' ,l [Time: Three Hours] Please check whether you have got the right question paper; 1. Question.No.l is compulsory. 2. Attempt any three from the remaining. -.;!, :.:: ,i: .i1. o,-.1 -l=-t, .l.l ,- 1'.rr- 11 r-'r', . . ),.,,1 '.i(II'r -.:+ . li J.'. . , i,-1 ' .'., : : i :. , I' ;151,, .,,' ..:'., ::':' ,;1 I ,,.. t'" '. ,:'1{s} I Marks:8O] (6) (6) (8) (s) /-\ .l (0) = 0,,' | : | = r is stationary if x=-sint, y=sint. tr/ \- / b) Evaluate J ,: 1l: .a':'2, ,x..; a>0,b>0 _', (.r- + a')(x- + b') c) Reduce the quadraticform x' -,2y.' + l0 z2 - t0 xy + 4xz hence, fihd its rank, index and signature and value class. ! 2zy to canonicalform and -1 z(z - l)(z - 2) ,! l.:: f't r r-1 .,. I L r r I lt Q.3.-,6) V9rif.y:Fy,ley,nr*lfto,n theqrem f_ar.,t' = .io t 0 i and hence find A-' & Ao fr t z) (6) (5) (8) (51 (6) e b)Using Residue theorem evaluate J -= _, n, where C is lzl=4. : : : r ,Z +7f lz 3l c) Find the singu ar va ue decomposition of L0 ,) F r t1 t-l at Q.4.a) lf a = i j, provethat3tanA=Atan3 l't rl 'l b) Find the sum of the,residues at singular points of .f G) = '2( ir\' /ar\'l Q.2.a)Showthatthefunctional I )r" -lLt *l-l l.rr;suchthat.r1o.1 = il \dt) \at11 1\67 7 OF26CF24EE'I 78689 58C4E IDFSD I 3
Transcript of *${r}wg ffi - Rasayani · Discuss any tw-e:i advantage of Lagrange's method over Newton's d ivided...
*${r}wg hT,l - ffi fiL****r# tul
Q.P. Code.: 1f8gz .. " :.1. r
2
Q.1.a) Find the extremalof f 9^ a..J ,,'2
b) ls 10,2,-+; a linear combination of v, = \t,2,2), v, = (3.4,6) :
[r 2 3) '' ' ''tt
c) Check whether , = i, I + i is derogatory or not.
d) Evaluate | ,' ,!, , along the parabola * = J.',l
[Time: Three Hours]
Please check whether you have got the right question paper;1. Question.No.l is compulsory.2. Attempt any three from the remaining.
-.;!,
:.::
,i:
.i1.
o,-.1 -l=-t,.l.l
,- 1'.rr- 11 r-'r',
. . ),.,,1
'.i(II'r -.:+. li J.'. . , i,-1
' .'., : : i :. , I'
;151,, .,,'..:'., ::':'
,;1I ,,..
t'" '.,:'1{s}
I Marks:8O]
(6)
(6)
(8)
(s)
/-\.l (0) = 0,,' | : | = r is stationary if x=-sint, y=sint.tr/\- /
b) Evaluate J
,: 1l:
.a':'2,,x..;
a>0,b>0_', (.r- + a')(x- + b')
c) Reduce the quadraticform x' -,2y.' + l0 z2 - t0 xy + 4xz
hence, fihd its rank, index and signature and value class.
! 2zy to canonicalform and
-1
z(z - l)(z - 2)
,!
l.::
f't r r-1.,. I L r r IltQ.3.-,6) V9rif.y:Fy,ley,nr*lfto,n theqrem f_ar.,t' = .io t 0 i and hence find A-' & Ao
fr t z)
(6)
(5)
(8)
(51
(6)
eb)Using Residue theorem evaluate J -= _, n, where C is lzl=4.
: : : r ,Z +7f
lz 3lc) Find the singu ar va ue decomposition of
L0 ,)F r t1t-l at
Q.4.a) lf a = i j, provethat3tanA=Atan3l't rl'l
b) Find the sum of the,residues at singular points of .f G) =
'2( ir\' /ar\'lQ.2.a)Showthatthefunctional I )r" -lLt *l-l l.rr;suchthat.r1o.1 =
il \dt) \at11
1\67 7 OF26CF24EE'I 78689 58C4E IDFSD I 3
Q.P. Code : Lt837...:,"-- :..
(8)
...1.
:!'
J-.
(.-.';t\.
(6)
.rr,,_,,+''...t.
' ';(.:
)-.
467 7 OF26CF 24887 78689 58C4E I DF8D I 3
Q.5. a) Find the extremum of I ext - y,', )d* .
b) Construct an orthonormal basis of R' using Gram$ = {(3,0,4),(-1,0,7 l,{2,9,1U1
Q.6. a) Find the linear transformation Y=AX
onto rr = Q,1,3)"Y, = (2,3,1)"y3 = (4'1'3)'
'. . . ?, :-.: ,.
abq-ut.z-=;,+,, ;:,.,-,i:,.'
ri. .
T1224 /T1028 ANALOG AND DIGITAL INTEGRATED CIRCUITS ,-.
'r" -., ). ;.,j--,: ii.' :.'1'
q1
/..:- ..:r: .. . .',.i. .::r.:.: ..'..: ,::....:tPlease check whether you have got the right question.paper.
N.B: 1. euestion No.1 is compulsory. l
2,AttemptanyThreequestionsoutremainingfivequestions'3. Assume suitable data if necessary and justify the same. , ,
Attempt any FOUR: |ZA
t',, . lt:: ,,t.:-.,-i ..i.,.., , j[,Mpil(qig0];. ' -
-j.l , , .'; 1l- .j;r' ,..'.,,,.', , --- ,:,t" ,t . - .):..,=:..,:.
,...,. ..:,: ,. t l:'.1.:r ':'-..,:i...' ..'.-, ,:::.:',.,':t,-,.,...
a. Discuss the characteristics of ideal op-amp. compare ideal and-p.r:6ttiiiettb. Draw and explain the functional block diagram of lC 55j;'r ,i :: ,t ',.:. ,.,: 1
d. What are shift registers? State its applications. ;'i:e.StatevariouscharacteristicsofdigitalICs...
[Time:3 Hours]
I circuits.
Q2. a.
b.
Q3. a.
b.
Q4. a.
b.
Q5. a.
b.
Q.6
10
10
10
10
10
10
i.!:' -
,: rj''n,
10
10
20a,
b.
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'1,!
F 9 78 F 8 CF4 9 4 AE2E, I 8F 29 7 D C3 427 EF 7 62
T 1224 I T l 029 NUMERTCAL METHODS AND OPTTMTZATTON TECHNTQUFS
(3 Hours)
Q.P. Code :16319
[Total Marks: 80
N.B.: ,1i':;,i:..'-.'.. Question No. 1 is compulsory. ,-.;.r,.1..r: 'i. '. Answer any three from the remaining five questions. :. ,
. Assume suitable data if necessary and justify the samgi,, -
. Figures to the right indicate the marks. +.f". '., , i
,.i)
,i i;ri,ti.r: r i;";lli-.- -. ,,r:l I i+ . +
Q1
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E
10
bc
d
Q2a
10Q3
06b
04
05
05
a Write the algorithm for computing a simple root of an equation f(x) = gusing False position method. Write any two comparison of this methodwith Secant method. Obtain a root for f(x):Zstnx-3x*2usingFalse position method. Consider the initial guesses as x=1 , xu=Z wherex is in radians and iterate until the relative error is less than 0.5%.
b Optimize Z=7xt-O3xf+Bxz-O.4xz2 subjected to the followingconstraint, g=4xr+5xz =100, using Lagrange's multiplier method.
c Solve the following LP problem using Graphical method.
Maximize Z=30xt+20x2
Subject to xr-xz 2 1 ; xr+x2 >3 ; xr, xz ) 0
: , -: ''. .
'of: .Picard's solve the following
'f iiill . .i
9780C43F3C299|2FC28278C3 I 73AE3 I 8
x=1 with a
Set upvalues:'
takes thethe cubic
estimate f(3).
a
Q4a
b
Q5a
b
Q6a
b
1.), ,'.J :':j! "tj
t ..'1..,,,- i
what is meant by interpolation? Discuss any tw-e:i advantage ofLagrange's method over Newton's d ivided differencq:,, Employ 1n-verseinterpolation of order 2 to determine the value of ,Xl that-corresponds to,.f(x)=9.93 for the following tabulated data. choose'.the sequeirle cij tne
'
points for your estimates to attain the best possible accuracy.r
T1224 tTt029
{qlor your estimates to attain the bestX 1 2 3F(x) 0.5 0.8 0.9
, .,1O-:"..'
^1r:l l.
' -ilei,
'i10
10
10
97 80C43F3C299 tzE C28278C3 I 73AE3 I 8
What is the advantage of multistepordinary differential equation?
Solve the equatione x2 - y2 =2using N.R. method. Perform 2
J -,- r:..:.i.: .., :.: ::::.!i. t;:..:.. ._11.: j.._..:_.:., .::,.,:,.;:ti,
*u I s€ ft1-w I cet' I ut* * I ,** tT t rlry ltxs"A. '- 'E f-S
Qr.
Qza)Q2 b)
....Please check whether you have got the right question paper.
N.B:1. Question No.l is compulsory2. Attempt any Three questions out of3. Assume suitable data if necessary and j.ustify th. ,.rn.
05
05
10
10
Q3 a)
Q3blWhat is String efflciencyA 3-phase .[3? KV,.t00t(t
10
'j:' ..ii r:': j;*; /..ai 'i t: lL
i!:,' ",
:Une,has.horizontal spacing with 3.5m l0,'dianieter is 1.2 cm. Find the tine
of single core cable.
i'X"= 0.15PU
= 0.15PU', X"= 0.15PU
KV, X"= 0.15PU
10
t0
Transformel Tl:1.25,,MV{,12.5 A/732y 1!, f,=jO.1 PU
Transfonnei,fl:, zg lvtvA, $A\/lt6 (!, f,=j0.1 pu.
Draw lmpedance diagram for the system choose base voltage of j.3z KV for thetransmission line and base voltampere of'20 MVA. Transmission line reactance =
r,]
1
4E2 1 DEFB9D6DC365 9OCFF89B87 8D I DA6
Answer the following questions.A) Explain Skin effect with diagram.
B) Prove that PU impedance ofwinding by selecting proper
C) Explain typicalACD) Cornpare overheadExplain effect on lineA ?00,Km lcngreactance of13.5MW at afind the sending r
inductivea load ofT circuit ,
1 String efficiency?
..,' '' |... '',\' ,,:"
N/m and the tension in the condueigii:
'.:
Explain different method ofAn overhead line over a riverabove water level. The
Solve any TwoExplain gradin$ExplainDerive
)<{
)(* )-=-*(\-,/
,)*/\I
A
. -,1 , :..",-",;:1.,', ,-ii;'. -,,,...." :. >t ,.iri\-'i:.-' i . ,-'i.' ,. : ii -:**.;.
' <),-. ;... .j . .. -;,11'.-i:r
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,...'., .:.; , 1:. . l_...'- 1 , -i1'
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I . . .,,ii..:':,',, '.. t'J't'
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alb)c) spacing.
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lr,$t^+ ,.:i-.$il' rJ^ ,.",r ^\ i
-,-rr .5' }yi,.? j\)";1 "$*8"-g:3.J')'.'tt-.-\r
i,::X......
' . .t rL']."*"t.rlr ,r." ri:i"t.ili .+:tr ..*.F .''L:c .l]' {::l:1i "_.+ - ir)I ' {
:il'
6€ sErn g EIEC c-B G-s m+H z-o t+
Q.1a)b)
c)
dle)
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Q.3 a)
Q.4 a)
b)
Q.5
.L s !a -r/ zot?*
T1224 I T1026 ELECTRICAL lr'{ACFllt'*ES I
Q.P. Code : 16505
[Tirne: Three Hours]
Please check whether you have got the right question paper.
N.B: 1. Question no 1 is compulsota.2. Attempt any THREE from the remaining questions'
3. Figures to right indicate full rnarks.
I Marks:8t?]
,qtternpt any four questions.Explain the use commutator in DC motor and genelator,'
Explain, haw the eore flux- set up in transformer is rnaintain constanl from no load to fiell ;oaci"
What are the drawbacks of three point starter €ompareto 1s'u1'l pcint st3iter.
What is the condltion at which transformer will have maximum efficiency.
Justify the sentence that we obtain lron loss from OC test and copper loss ii-om SC test.
Derir,re the expression for iorque developed in singly excrted rnagnetic fleid.
What is conrmutation anci expiain the process of commutation in DC generator. Also mention the
methods to inrprove the commutation process.
t0sl{0s}{0s}{05}(0s)
(10)
{10}
(10)
{1CI}
{10}(10)
Derive an expression for copper saving in auto transformer' U0)Two sir-:gle phase transformers ivhich have the same turns ration irre connected in parallel and supplv a (10)
total Ioaci r:f 800 kW at 0,8 p f. lagging. The rating are as foilsws,
Dete
Rating , u resistances p"u reactances
Transformer: A 400Kl/A 0.02 0.04
Transfoi mer B 5OO'KVA 0.01 0,05
rrn,ine the power 0utp.ut factor of each transformer
Write short notes on i :' .'
:-(x0l
b)
a)
b)
,; r..r.lt:,ri'.'t ll '.
: ,."',, ,f, ,,
Qr6',i),Strp p nE r4s' Test o 6'qin g! e p:liaSe transforme r.
ii) Electiicaf 6iafile m'e.th_od'sib'r separately excited DC motor'
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T1224 /TiO27 S.E.(ELECTRICAL ENGGXSEM IV) (CBSGS) SIGNAL i'ROCESSING
{IBoura}
H:B IlQl i$oomptrory.
$ tutemp ury threr rymthm &om rmrfufug &slioms3). *s*nrc $dtdbl* de ffltu$vw,ryuird.
Q.P.Code:016114
Tsi*t ilIerlf,*l S0
al) a) $at* and provs diffcratidion prop,rty of rrfiausftrrn.
t5*4:
c) Deteanirre 0re *Ubilitf frad cflrsattty afthn csm derdbd by
H{z}= ild#:r- + ffi f6nocr}s<Ff .(z
* CM ik $rnbiHty rnd ttuc iat arianre pqrty +f the qr*Um yhl * x [-n]Q2) s) Find thc evea aild odd coqpomfis ofx[uJ = {_I, ?12,317,6,
b) Sind the initlat value atrd SmI ffilus of
xr*)*Erfu noep;r1
r) Find rho ffipss$a y (rlof m ITI a;rsrcn ]f Orap*1asg
r0l
$) a) tvllrrtdop*meanbrRoc?Menlioutkedgmlfisanee. ridthgscofirfiaitgdruarl*rLeIt sid$d sigunl.
b) Hrrd ttp Fourier trandorm afx (t) * s-& u (g-A)
c) Clreck ra{rstlrsr thc givan sigrsl x (t} = sinsr++t is pqury sfrgnEl or ast"d) Obtain the a-tmnsf,orm cfx (rr) * {n I} u {rr}
l* {- t*FtrsTknLr &t7
t05I
I05l
l
[s*4I
x {t}and h(f} ers.
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b) fixpre*a ttre givm *ignd 1 {t},qsing basis furetiog&
T1224 1r102? S.E.(ELECTRICAL ENGGXSEM IV) (CBSGS) SIGNAL PROCESSING
Q.P.Code:016114
2
Qif c) Firrtt the phasa and aragRiarde ffilorm of rhs sys(ern h(n)* [1"1l}] (I0M)
b}Acau${tllTIsystemlgdc$efibdbyt}rediffmrctequ***rr.$sI{}
y (n)-314y(n'1!rll8y(u'$*u(nlru(u-U 'fisd fts forced rcfipsas +f tttc tystem
due to steP inPut-
eS a)FindtneEtrassfonxtofthegiveusiffil*(n) :1" ffi $SM)
b)&$ dixrr.ute time LTI system gove$les by the difBr€*'$s equatiou"* {Iotvt}
Y {n} * x (*) t S-8 x (n-l} + S'S x {n-4 - $'ag y{tt'2}'
Detqmrine the trausfkr fiinctics. sketch tln prlo znm plot on the E pl*na
oG elAn I rroint eequerre ie grven hy x(E)=t 13'3'a$*3'2't ) 'Comprrie I point BFT of (10M1
x(nl rry nrdix -2 bIT -FFT method'
b) pctfbrm ttrs *ieularcouwl*ion$*ineDrT.Xr(nFt&t,ttl letnts{1'43'4} (I0}d}
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