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Engineering mat&ematic" '()* +!e"tion paper
Engineering mat&ematic" '()* +!e"tion paper
Question 1Question 1
If every minor of order r of a matrix is zero, then rank of is If every minor of order r of a matrix is zero, then rank of is
lleesss s tthhaan n oor r ee!!uuaal l tto o r r " " ee!!uuaal l tto o r r C C ##rreeaatteer r tthhaan n r r D D lleesss s tthhaan n r r Question $ Question $
The system %& ' of e!uations is consistent if The system %& ' of e!uations is consistent if
ddeet t ( ( '' "
" ) ) ddeet t & & '' C
C iis s nnoonn* * ssiinn##uullaar r D
D iis s oorrtthhoo##oonnaall Question +
Question +
If +x $y z &', x -y z & ', $x y -z & ' is a system of e!uations, then If +x $y z &', x -y z & ', $x y -z & ' is a system of e!uations, then
iit t iis s iinnccoonnssiisstteenntt "
" it it hahas s ononly ly ththe te tririvivial al ssololuutition on x & x & ', ', y y & '& ', z , z & '& ')) C
C dedetetermrmininanant ot of tf thhe me matatririx ox of cf coeoefffificicienents ts is is zezeroro D
D It It can can .e .e redreducuced ed to to a sa sinin#l#le ee e!u!uatiation on anand sd so so sololututioion dn doeoes ns not ot exexisistt Question
Question
-"y eliminatin# constants a and . from z & a/x y0 ., the artial differential e!uation formed is "y eliminatin# constants a and . from z & a/x y0 ., the artial differential e!uation formed is ! ! & & 11 " " 22! ! & & 11 C C 2 2 ! ! & & '' D D ! ! & & '' Question 3 Question 3
The value of div /#rad f0, where f & tan*1 /y 4 x0 is The value of div /#rad f0, where f & tan*1 /y 4 x0 is *1*1 " " '' C C 11 D D $$ Question 5 Question 5
The work done .y the force 6 & yz I zx k, in movin# a articular from the oint /1, 1, 10 to the The work done .y the force 6 & yz I zx k, in movin# a articular from the oint /1, 1, 10 to the oint /+, +, $0 alon# a ath C
--" " 1'1' C C 1717 D D 1- 1-Question 7 Question 7
"ilinear transformation always transforms circles into "ilinear transformation always transforms circles into ssttrraaii##hht t lliinneess " " eelllliisseess C C aarraa..oollaass D D cciirrcclleess Question 8 Question 8
If 6/s0 6ourier transform of f/x0, then the 6ourier transform of f/ax0 is If 6/s0 6ourier transform of f/x0, then the 6ourier transform of f/ax0 is aa66//ss44aa00 " " 1144a a 66//aass00 C C 1144a a 66//ss44aa00 D D aa66//aass00 Question 9 Question 9
The sufficient conditions for the conver#ence of iteration method is The sufficient conditions for the conver#ence of iteration method is
ththe ce co* o* efeffificicienent mt matatririx ix is a s a rereal al sysymmmemetrtric ic mmatatririxx "
" ththe ce co* o* efeffificicienent mt matatririx ix is a s a ddiaia#o#onanalllly dy domomininanantt C
C ththe e auau#m#menenteted d mmatatririx x is is an an ororththoo#o#onanal l mamatrtrixix D
D ththe ce co* o* efeffificicienent mt matatririx x is is a sa syymmmmetetriric mc matatririxx Question 1'
Question 1'
The n th divided difference of a n th de#ree olynomial is a The n th divided difference of a n th de#ree olynomial is a
oollyynnoommiiaal l oof f ddee##rreee e mmoorre e tthhaan n 11 "
" oollyynnoommiiaal ol of df dee##rreee me moorre te thhaan n $$ C
C oollyynnoommiiaal ol of df dee##rreee me moorre te thhaan n '' D
D ccoonnssttaanntt Question 11 Question 11
What is the order of :un#e 2 kutta method is a modified ;uler<s method= What is the order of :un#e 2 kutta method is a modified ;uler<s method= ++ " " --C C $$ D D 11 Question 1$ Question 1$
If the two re#ression co* efficients are *')- and *')9, then the correlation co*efficient is If the two re#ression co* efficients are *')- and *')9, then the correlation co*efficient is ''))55 " " ''))++55 C C >>''))55 D D **''))55 Question 1+ Question 1+ If some of the
If some of the ei#en values of the ei#en values of the matrix matrix of the !uadratic of the !uadratic form the ositive and others ne#ative,form the ositive and others ne#ative, then !uadratic form is
then !uadratic form is
oossiittiivve e sseemmi i ddeeffiinniittee "
C
C nnee##aattiivve e sseemmi i ddeeffiinniittee D
D nnee##aattiivve e ddeeffiinniittee Question
Question
1-?in#ularity of zez14$ at z & 'is of the tye ?in#ularity of zez14$ at z & 'is of the tye
iissoollaatteed sd siinn##uullaarriittyy "
" rreemmoovvaa..lle e ssiinn##uullaarriittyy C
C eesssseennttiiaal l ssiinn##uullaarriittyy D
D iissoollatateed d aannd d rrememoovvaa..lle e ssiinn##uullarariititieess Question 13
Question 13
The rate of conver#ence is the @auss 2 ?eidal method is AAAAAAAas fast as in @auss* The rate of conver#ence is the @auss 2 ?eidal method is AAAAAAAas fast as in @auss* Baco.i<s method)
Baco.i<s method)
tthhrriiccee "
" hhaallff* * ttiimmeess C
C ttwwiiccee D
D tthhrreee e ..y y ttwwo o ttiimmeess Question 15
Question 15
In alication of ?imsons 14+rd rule, the interval h for closer aroximation should .e In alication of ?imsons 14+rd rule, the interval h for closer aroximation should .e
ssmmaallll "
" ooddd d oor r llaarr##ee C
C llaarr##ee D
D eevveen n aannd d ssmmaallll Question 17
Question 17
Which of the followin# is a ste .y ste method= Which of the followin# is a ste .y ste method=
TTaayylloorr<<s s mmeetthhoodd "
" PPiiccaarrdd<<s s mmeetthhoodd C
C ddaamm<<s s ""aassh h ffoorrtth h mmeetthhoodd D
D ;;uulleerr<<s s mmeetthhoodd Question 18
Question 18
The resultant of a colanar concurrent force system will have the same moment as the sum of The resultant of a colanar concurrent force system will have the same moment as the sum of moments of each force and is known as
moments of each force and is known as
aarrii##nnoonn<<s s tthheeoorreemm "
" aammee<<s s tthheeoorreemm C
C PPaauus s aannd d @@uullddiinnuus s tthheeoorreemm D
D PPrriinncciille e oof f ttrraannssmmiissssii..iilliittyy Question 19
Question 19
The maximum tension is the .elt, for limitin# friction conditions, occurs at The maximum tension is the .elt, for limitin# friction conditions, occurs at
ssttaarrttiinn## "
" ssttooiinn## C
C mmaaxxiimmuum m oowweer r sseeeedd D
D sseecciiffiic c sseeeedd Question $'
Question $'
Which one of the followin# airs of henomena illustrates the article asect of wave article Which one of the followin# airs of henomena illustrates the article asect of wave article duality=
duality=
CCoommttoon n ;;ffffeecct t aannd d ""rraa####<<s s llaaww "
C
C CCoommttoon n ;;fffefect ct anand d auaulli<i<s s rriinncicilele D
D ""rraa####<<s s llaaw w aannd d hhoottooeellececttriric c eefffefecctt Question $1
Question $1
The oeration of the laser is .ased on The oeration of the laser is .ased on
TThhe e uunncceerrttaaiinntty y rriinncciillee "
" TThhe e eexxcclluussiioon n rriinncciillee C
C IInndduucceed d eemmiissssiioon n oof f rraaddiiaattiioonn D
D IInntteerrffeerreenncce e oof f mmaatttteer r wwaavveess Question $$
Question $$
Durin# roa#ation of ultrasonic wave, if there is a ri#id wall .etween two media, the incident Durin# roa#ation of ultrasonic wave, if there is a ri#id wall .etween two media, the incident wave is
wave is
ccoommlleetteelly ty trraannssmmiitttteedd "
" ccoommlleetteelly y rreefflleecctteedd C
C aarrttly ly rerefflleectcteed ad annd d aarrttly ly ttrrananssmmiitttteedd D
D ccoommlleetteelly y aa..ssoorr..eedd Question $+
Question $+
:adio#rahic insection is .ased on :adio#rahic insection is .ased on ddiiffffeerreennttiiaal l aa..ssoorrttiioonn " " ddiiffffrraaccttiioonn C C iinntteerrffeerreennccee D D fflluuoorreesscceennccee Question Question
$-@lass* ceramics are o.tained .y @lass* ceramics are o.tained .y
coconnttrroolllleed d hheeat at ttrreeatatmmenent t oof f cceerarammiiccss "
" ccoonnttrroolllleed d hheeaat t ttrreeaattmmeennt t oof f ##llaassss C
C mmiixxiinn# # ##llaasss s oowwddeer r wwiitth h cceerraammiiccss D
D mmeellttiinn# a# annd cd coooolliinn# t# thhe re raaw mw maatteerriiaall Question $3
Question $3
The transition from the ferroma#netic to the arama#netic state is named after The transition from the ferroma#netic to the arama#netic state is named after CCuurriiee " " CCuurriiee* * WWeeiissss C C EEeeeell D D DDee..yyee Question $5 Question $5 Pure silicon at F G is an Pure silicon at F G is an
iinnttrriinnssiic c sseemmiiccoonndduuccttoor r "
" eexxttrriinnssiic c sseemmiiccoonndduuccttoor r C C mmeettaall D D iinnssuullaattoor r Question $7 Question $7
The ma#netization of a suerconductor is The ma#netization of a suerconductor is '' " " 2"2" C C *1*1 D D 2H2H Question $8 Question $8
t room temerature, fracture of ceramic materials almost always occur .y t room temerature, fracture of ceramic materials almost always occur .y
sslloow w rrooaa##aattiioon n oof f ccrraacckkss "
" llaassttiic dc deeffoorrmmaattiioonn C
C slsloow w roroa#a#atatioion on of cf crarackcks as and nd llasastitic dc defefoormrmatatioionn D
D ffaasst t rrooaa##aattiioon n oof f ccrraacckkss Question $9
Question $9
6or sta.le e!uili.rium of floatin# .odies, the centre of #ravity has to .e always 6or sta.le e!uili.rium of floatin# .odies, the centre of #ravity has to .e always
..eelloow w tthhe e cceennttrre e oof f ..uuooyyaannccyy "
" aa..oovve e tthhe e cceennttrre oe of f ..uuooyyaannccyy C
C aa..oovve e tthhe e mmeettaacceennttrree D
D ..eelloow w tthhe e mmeettaacceennttrree Question +'
Question +'
n oil of kinematic
n oil of kinematic viscosity ')$3 stokes flows throu#h a ie of 1' cviscosity ')$3 stokes flows throu#h a ie of 1' cm diameter) The flow ism diameter) The flow is critical at a velocity of a.out
critical at a velocity of a.out ''))3 3 mm44ss " " 11))3 3 mm44ss C C $$))8 8 mm44ss D D --))5 5 mm44ss Question +1 Question +1
Water is to .e lifted .y a net head of 18'm) Identical ums with secific seed of +', rotational Water is to .e lifted .y a net head of 18'm) Identical ums with secific seed of +', rotational seed of 1-3' rm and caa.le of dischar#in# $'' liters er second are availa.le) The num.er of seed of 1-3' rm and caa.le of dischar#in# $'' liters er second are availa.le) The num.er of ums re!uired is ums re!uired is 11 " " $$ C C ++ D D --Question +$ Question +$
The "FD3 of waste water
The "FD3 of waste water is determined to .e is determined to .e 13'm#4 at $''C) The k value is known to .e ')$+13'm#4 at $''C) The k value is known to .e ')$+ er day
er day) What would .e ultimate "FD=) What would .e ultimate "FD= 1188' ' mm##44 " " $$''3 3 mm##44 C C $$$$' ' mm##44 D D $$33' ' mm##44 Question ++ Question ++
Fn no* load the efficiency of a distri.ution transformer is #overned .y the Fn no* load the efficiency of a distri.ution transformer is #overned .y the
rerelalatitive ve mama#n#nititududes es of of ththe ce corore le lososs as and nd ththe ce cooeer lr lososss "
" mmaa##nniittuudde e oof f tthhe e ccoorre e lloossss C
C mmaa##nniittuudde e oof f tthhe e rriimmaarry y vvoollttaa##ee D
D mmaa##nniittuudde oe of tf thhe se seeccoonnddaarry y vvoollttaa##ee Question
Question
+-The urose of includin# an external resistance at the time of startin# a DC motor is to The urose of includin# an external resistance at the time of startin# a DC motor is to
iinnccrreeaassees s tthhe se sttaarrttiinn# # ttoorr!!uuee "
" iinnccrreeaasse e tthhe e aarrmmaattuurre e fflluuxx C
C rreedduucce te thhe se sttaarrttiinn# c# cuurrrreenntt D
D mmaaiinnttaaiin n tthhe e ccoonnssttaannt t fflluuxx Question +3
Question +3
Which of the followin# can .e used to extend the ran#e of an ammeter= Which of the followin# can .e used to extend the ran#e of an ammeter=
lolow w reresisiststanance ce is is seseriries es wiwith th ththe e amammmeteter er "
" hhi#i#h h reressisistatannce ce is is seseriries es wiwith th ththe e amammmeteter er C
C lolow w reresisiststanance ce in in aararallllel el wiwith th ththe ae ammmmeteter er D
D hhi#i#h h reressisistatannce ce in in araralallelel wl witith th thhe ae ammmmeteter er Question +5
Question +5
;rror due to imroer zero adustment classified as ;rror due to imroer zero adustment classified as
ooeerraattoor r eerrrroor r "
" eennvviirroonnmmeennt t eerrrroor r C
C iinnssttrruummeennt t eerrrroor r D
D rraannddoom m eerrrroor r Question +7
Question +7
The ratin# of transformer is reresented in The ratin# of transformer is reresented in GWGW " " GGWWHH C C GG D D oollttaass Question +8 Question +8
Jutual inductance is define as the ratio of chan#e of Jutual inductance is define as the ratio of chan#e of
flfluux ix in cn cooiil 1 l 1 tto to thhe ce chhaann##e oe of ff flluux ix in cn cooiil $l $ "
" cucurrrrenent it in cn coioil 1 l 1 to to ththe ce chhanan##e oe of cf cuurrrrenent it in cn coioil $l $ C
C flfluux x in in cocoil il 1 1 to to ththe e chchanan#e #e oof f cucurrrrenent it in n cocoil il 11 D
D flfluux cx cooil il $ t$ to to thhe ce chhaann##e oe of cf cuurrrreennt it in cn cooiil 1l 1 Question +9
Question +9
What is the work done .y air which enters into an evacuated vessel from atmoshere when the What is the work done .y air which enters into an evacuated vessel from atmoshere when the valve is oened= The atmosheric ressure is 1)'1+ .ar and 1)3 m+ of air at atmosheric condition valve is oened= The atmosheric ressure is 1)'1+ .ar and 1)3 m+ of air at atmosheric condition enters into the vessel)
enters into the vessel) 11''''))$ $ kkBB " " 11$$''))3 3 kkBB C C 11--''))553 3 kkBB D D 113311))993 3 kkBB Question -' Question -'
Jost of the ener#y #enerated in the en#ine of a car is reected to the air .y the radiator thou#ht the Jost of the ener#y #enerated in the en#ine of a car is reected to the air .y the radiator thou#ht the circulatin# water) ?hould the radiator .e analyzed as
circulatin# water) ?hould the radiator .e analyzed as
a a cclloosseed d ssyysstteemm "
" aan n ooeen n ssyysstteemm C
C aan n iissoollaatteed d ssyysstteemm D
D ccoomm..iinnaattiioon n oof f //0 0 aannd d //""00 Question -1
Question -1
Gelvin 2Planck<s law deals with Gelvin 2Planck<s law deals with
ccoonnsseerrvvaattiioon n oof f eenneerr##yy "
" ccoonnsseerrvvaattiioon n oof f hheeaat t iinntto o wwoorrk k C
C ccoonnsseerrvvaattiioon n oof f wwoorrk k iinntto o hheeaatt D
D ccoonnsseerrvvaattiioon n oof f hheeaatt Question -$
Question -$
To increases the work caacity of ener#y transferred .y heat transfer from hi#h temerature to low To increases the work caacity of ener#y transferred .y heat transfer from hi#h temerature to low temerature the
temerature the
lolowewer tr tememeeraratuture re shshouould ld .e .e lolowewered red kekeeeinin# t# tememeeratraturure de dififferferenence ce sasameme "
" hihi#h#her er temtemeeratraturure se shohoululd .d .e ie incncrereasased ed kekeeeinin# t# tememeeratraturure de dififfeferenrence sce samamee C
C tetemmeeraratuture re didifffefererennce ce sshohoululd d .e .e inincrcreaeasseded D
D tetemmeeraratuture re didifffefererennce ce sshohoululd d .e .e ddececrereasaseded Question -+
Question -+
The characteristic e
The characteristic e!uation of #ases & m:T holds #ood for!uation of #ases & m:T holds #ood for
mmoonnoo* * aattoommiic c ##aasseess "
" ddiiaattoommiic c ##aasseess C C rreeaal l ##aasseess D D iiddeeaal l ##aasseess Question Question
--"ooths al#orithm is used for "ooths al#orithm is used for
ffllooaattiinn# # ooiinnt t ddiivviissiioonn " " rreessttoorriinn# # ddiivviissiioonn C C iinnttee##eer r mmuullttiilliiccaattiioonn D D ss!!uuaarre e rroooott Question -3 Question -3
Which of the followin# addressin# modes is
Which of the followin# addressin# modes is convenient to handle ointers=convenient to handle ointers=
iimmmmeeddiiaatte e aannd d ddiirreecct t aaddddrreessssiinn## " " iinnddiirreecct at addddrreessssiinn## C C ..aasse e aaddddrreessssiinn## D D rreellaattiivve e aaddddrreessssiinn## Question -5 Question -5
Which one of the followin# is false a.out Pielinin#= Which one of the followin# is false a.out Pielinin#=
InIncrcreaeaseses s ththe e CCPK PK ininsstrtruuctctioion n ththrorouu#h#huutt "
" :e:eduduceces s ththe ee exexecucutition on titime me of of an an inindidivividudual al ininststruructctioionn C
C IInnccrreeaassees s tthhe e rroo##rraam sm seeeedd D
D //0 0 aannd d //""00 Question -7
Question -7
What is the outut of the followin# code fra#ment for n& -=Int sum/n0Int nLMif /nNltL10return nLelse What is the outut of the followin# code fra#ment for n& -=Int sum/n0Int nLMif /nNltL10return nLelse return /n sum/n*100L O return /n sum/n*100L O 1'1' " " 1515 C C 1- 1-D D 1313 Question -8 Question -8
What is the outut of the followin# code=Jain/ 0M int i&+While /i**0MInt What is the outut of the followin# code=Jain/ 0M int i&+While /i**0MInt i&1''Li**Lrintf/<d))R,i0LOO
i&1''Li**Lrintf/<d))R,i0LOO
iinnffiinniitte e lloooo "
" ccoommiillaattiioon n eerrrroor r C C 9999))))9999))))9999)))) D D ++))))$$))))11)))) Question -9 Question -9
Which of the followin# statements re#ardin# the adsortion of a #as on a solid is not correct= Which of the followin# statements re#ardin# the adsortion of a #as on a solid is not correct=
ThThe ame amouount nt of of #a#as as adsdsoror.e.ed id incncrereasase we witith ih incncrereasase is e is rresessusurere "
" ThThe ame amouount ont of #af #as as adsdsoror.e.ed dd dececrereasases es wiwith th inincrcreaeaseses in s in tetemmereratatururee C
C ThThe ame amouount nt of of #a#as as adsdsoror.e.ed dd decrecreaeaseses ws witith ih incncrearease se in in ththe are area oea of tf the he a.a.sosor.r.enentt D
D ththe ade adsosorrtition ion is as accccomomaaninied .ed .y dy dececrereasase in e in enentrtrooy oy of thf the sye syststemem Question 3'
Question 3'
The secific rate constant of a first order reaction deends on The secific rate constant of a first order reaction deends on
ccoonncceennttrraattiioon n tto o tthhe e rroodduucctt "
" ccoonncceennttrraattiioon n oof f tthhe e rreeaaccttaanntt C C tteemmeerraattuurree D D ttiimmee Question 31 Question 31
The total num.er of vi.rational de#rees of freedom of hydro#en eroxide molecule is The total num.er of vi.rational de#rees of freedom of hydro#en eroxide molecule is
sseevveenn "
C C ffoouur r D D nniinnee Question 3$ Question 3$
The increasin# order of .oilin# ran#e for etroleum fractions is #iven .y The increasin# order of .oilin# ran#e for etroleum fractions is #iven .y
nnaahhtthha a NNllttL L ##aassoolliinnee "
" #a#asosoliline ne NlNltL tL nanahththha Na NltltL kL kereroosesenne Ne NltltL dL dieiessel el ooilil C
C kekerorossenene Ne NltltL nL naahhththa Na NltltL #L #asasololinine Ne NltltL dL dieiessel el ooilil D
D nanahhththa Na NltltL #L #asasololinine Ne NltltL dL dieiesesel ol oil Nil NltltL kL kererososenenee Question 3+
Question 3+
et z & ax .y xy where a and . are ar.itrary constants and x, y are indeendent varia.les) The et z & ax .y xy where a and . are ar.itrary constants and x, y are indeendent varia.les) The differential e!uation which is related to the a.ove is
differential e!uation which is related to the a.ove is
orordidinnarary y ddififfefererenntitial al e!e!uuatatioionns s wiwith th orordeder $r $ "
" orordidinnarary y ddififfefererenntitial al e!e!uuatatioion n wiwith th orordeder r 11 C
C aarrttiial al ddififfeferreennttiial al ee!!uuatatiioon wn wiitth oh orrddeer $r $ D
D aartrtiaial l ddififfefererentntiaial l e!e!uuatatioion n wiwith th oordrder er 11 Question
Question
3-The volume .ounded .y the cylinder x$ y$ & -, and the lane y z & + and z & ' is The volume .ounded .y the cylinder x$ y$ & -, and the lane y z & + and z & ' is 11$$SS " " 5S5S C C +S+S D D SS Question 33 Question 33
The value of the inte#ral /x 2 $y0 dx xdy taken over the circle x$ y$ & 1 is The value of the inte#ral /x 2 $y0 dx xdy taken over the circle x$ y$ & 1 is -S-S " " +S+S C C $S$S D D SS Question 35 Question 35
et f/z0 & u iv .e an analytic function, which of the followin# statement are correct=I) "oth u and et f/z0 & u iv .e an analytic function, which of the followin# statement are correct=I) "oth u and v satisfy alace e!uationII) 6amily of curves u & c1 and v & c$ cut ortho#onallyIII) ux & *vy and v satisfy alace e!uationII) 6amily of curves u & c1 and v & c$ cut ortho#onallyIII) ux & *vy and uy & vzI
uy & vzI) u 2 iv ) u 2 iv is also an analytic is also an analytic functionfunction
//II0 0 aannd d //IIII0 0 oonnllyy "
" //II00, , //IIII0 0 aannd d //IIIIII0 0 oonnllyy C
C //II00, , //IIII0 0 aannd d //II0 0 oonnllyy D
D //IIII00, , //IIIIII0 0 aannd d //II0 0 oonnllyy Question 37
Question 37
ariance of the ariance of the random varia.le % is -) random varia.le % is -) It<s mean is $) Then ;/x$0 isIt<s mean is $) Then ;/x$0 is $$ " " --C C 55 D D 88 Question 38 Question 38
The marks secured .y 5'' students in a Jathematics test were normally distri.uted with mean 33) The marks secured .y 5'' students in a Jathematics test were normally distri.uted with mean 33) If 1'' students #et marks a.ove
If 1'' students #et marks a.ove 73, the num.er of students securin# marks 73, the num.er of students securin# marks .etween +3 and 33 is.etween +3 and 33 is
" " $$'''' C C ++'''' D D 33'''' Question 39 Question 39 If is a - x
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If f/z0 & u iv an analytic function and u and v are harmonic, then u and v will satisfy If f/z0 & u iv an analytic function and u and v are harmonic, then u and v will satisfy
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