GATE Civil Engineering Solved 2011

8/13/2019 GATE Civil Engineering Solved 2011

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2011 CEQ. 1 Q. 25 carry one mark e h.

Q.l [A] is a square matrix which is neither symmetric nor skew-symmetric and [A)T is its transpose.The sum and difference of these matrices are defined as [S] = [A] + [A]T and [D] = [Al - [Af ,respectively. Which of the following statements is TRUE?A) Both [S] and [D] are symmetricB) Both [S] and [D] are skew-symmetricC) [S] is skew-synunetric and [D) is symmetricD) [S] is symmetric and [D] is skew-symmetric

Q.2 The square root of a number N is to be obtained by applying the Newton Raphson iterations to theequation x 2 N =0. If i de notes the iteration index, the correct iterative scheme wil l beA) x i+ l = . x;+ N J2 X 2 N JB) x1+1 x1 - ,2 x

1 N 2 JC) x1+1 x12 X D) x. 1 =_ _ x.- NJI 2 I X;Q.3 There are two containers, with one containing 4 Red and 3 Green balls and the other comaining

3 Blue and 4 Green balls. One ball is drawn at random from ~ c h container. The probability thatone of the balls is Red and the other is Blue will be A) 1/7 B) 9/49 C) 12/49

Q.4 For the fillet weld of size s shown in the adjoiningfigure the effective throat thickness is

A) 0.61 s B) 0.65 s C) 0.70 s

D) 3/7

D) 0.75 s

Q.S A 16 nun thick p late measuring 650 nun x 420 mm is used as a base plate for an ISHB 300 columnsubjected to a factored axial compressive load of 2000 kN. As per IS 456-2000, the minimum gradeof concrete that should be used below the base plate for safely ca rrying the load isA) M15 B) M20 C) M30 D) M40

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2011 CEQ.6 Consider a reinforcing bar embedded in concrete. In a marine environment this bar undergoes

uniform corrosion, which leads to the deposition of corrosion products on its surface and anincrease in the apparent volume of the bar. This subjects the surrounding concrete to expansivepressure. As a result, corrosion induced cracks appear at the surface of concrete. Which of thefollowing statements is TRUE

Q.7

A) Corrosion ca uses circumferential tensile stresses in concrete and the cracks will be parallel tothe corroded reinforcing bar.B) Corrosion causes radial tensile stresses in concrete and the cracks will be parallel to thecorroded reinforcing bar.

C) Corrosion causes circumferential tensile stresses in concrete and the cracks will beperpendicular to the direction of the corroded reinforcing bar.

D) Corrosion causes radial tensile stresses in concrete and the cracks will be perpendicular to thedirection of the corroded reinforcing bar.

The results for sieve analysis carried out for three typesof sand, P, Q and R, are given in the adjoining figure. If thefineness modulus values of the three sands are given asFMp, FM0 and FMR, it can be stated that

A)FMo= .JFM.PxFMRC) FMp> FMo> FMR

B) FM 0 =0.5 (FMp + FMR)D) FMp < FM0 < FMR

Sieve size

Q.8 The cross-section of a thermo-mechanically treated TMT ) reinforcing bar has

Q.9

C E

A) soft ferrite-pearlite throughout.B) hard martensite throughout.C) a soft ferrite-pearlite core with a hard martensitic rim.D) a hard martensitic core with a soft pearlite-bainitic rim.

Consider a simply supported beam r r ~ r ~ ~with a uniformly distributed loadhaving a neutral axis NA) as shown.For points P on the neutral axis) andQ at the bottom of the beam) the stateof stress is best represented by whichof the following pairs?A)

(C)

L

B)

(D)

Q + p L

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20 CEQ.lO For a saturated sand deposit, the void ratio and the specific gravity of solids are 0.70 and 2.67,respectively. The critical (upward) hydraulic gradient for the deposit would be

(A) 0.54 (B) 0.98 C) 1.02 (D) 1.87Q.ll Likelihood of general shear fa ilure for an isolated footing in sand decreases with

A) decreasing footing depth(B) decreasing inter-granular packing of the sand(C) increasing footing widthD) decreasing soil grain compressibi lity

Q.l2 For a sample of dry, cohesionless so il with friction angle,, the failure plane will be inclined to themajor principal plane by an angle equal to(A)>

Q.l3 Two geometrically identical isolatedfootings, (linear elastic) and Y rigid), areloaded identically (shown alongside). Thesoi l reactions wi ll ., l s p t r : o P i c J i n e ~ r . , t a s t i e s o i l-:,-:.:- . . . :--,:

Uniform pressure

A) be uniformly distributed for but not fo r(C) be uniformly distributed for both and Y

(B) be uniformly distributed for but not for YD) not be uniformly distributed for both and Y

Q.l4 A soil is composed of solid spher ical grai ns of identical specific gravity and diameter between0.075 mm and 0.0075 mm. f the terminal velocity of the largest particle falling through waterwithout flocculation is 0.5 rnm/s, that for the smallest particle would beA) 0.005 mm/s (B) 0.05 mm/s C) 5 mm/s D) 50 mm/s

Q.l5 A watershed got transformed from rural to urban over a period of time. The effect of urbanizationon storm runoff hydrograph from the watershed is to(A) decrease the volume of runoff(C) decrease the time base

(B) increase the time to peak discharge(D) decrease the peak discharge

Q.l6 For a given discharge, the critical flow depth in an open channel depends on(A) channel geometry only(B) channel geometry and bed slope(C) channel geometry, bed slope and roughness(D) channel geometry, bed slope, roughness and Reynolds number

Q.l7 For a body completely submerged in a fluid, the centre of gravity (G) and centre of Buoyancy 0)are known. The body is considered to be in stable eq uilibrium if

E

(A) 0 does not coi ncide with the centre of mass of the displaced fluid(B) G co incides with the centre of mass of the displaced fluid(C) 0 lies below G(D) 0 lies above G

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2 11Q.l8 CEThe fl owina hori zontal . fric tio nle ss recta ngula rope nchannel is supercriti ca l Asm ooth hum pisbuilt onth e channel floor.As theheig ht ofhum p isin creased ,chokedcondit ion isat ta ined. W ithfu rther in cr eas ein the height ofthehu mp, the wate rsurfacewill

(A)rise at a sectio n upstr eam ofth e hum pC) dropat th ehump

(B )dropata sectio nupstr eam ofthe hum p(D)ri se at thehum p

Q.l9 Consid er th e followin g unit pro cesse s com m only us edinw ater tre atm ent; rapid mix in g (R M ),flocculation (F ). pri m ary sedim enta tio n (PS), secondary sed im enta t ion (SS), ch lorin at ion C) andrapid sand fil trat ion (R SF). Theorder of these uni t pro cesses(first to last)inaconven tio nalwate rtr eatm entplantis

Q .20

(A )P S ~ R S F ~ F ~ R M ~ S S ~ (C) P S ~ F ~ S S ~ R S F ~ R M ~

(B) S ~ F ~ R M ~ R S F ~ S S ~ (D) PS RM F SS R SF C

Anaerobically treat ed efflu entha s PNofto tal coli form as 106 I 100mL A fter chlorinati on,th ePNvalue decli nesto102 / 100mL Thepercentre m ova l( R ) andlog rem ova l(logR)of to talcolif orm MPNis(A ) R=99.9 0; logR =4(C ) R =99.9 9;logR= (B) R=99.9 0;logR=(D ) R=99 .9 9; logR=2

Q.21 Consider fou r com m onai rpolluta n tsfo un d in urb an environm ents, N O , 502 S oo t and0 3. A m ongth esewhich on is the secondary air pollu ta nt? (B ) NO (D )Soo t

Q.2 2 Theprobabili ty thatknum berofveh icl es arr iv e(i.e.cross apredefined line) intimet is givenasAt)k e J jk,whereA is th e average vehic le ar riv al rat e. W hat istheprobabili ty that the tim eheadwayisgreate rtha nor equaltotim et 1?C) i'

Q .23 Avehicle negoti ate satr ansiti on cu rve withunif orm speed v. fth e radius ofthe hor iz ont al cu rveand theallow able jerk areRand1 respectively , the m inim um lengthofthe transiti on c ur veis

Q .2 4 In M arshalltest ingofbitum in ous mix es ,asthe bitum en conte ntin cre ases thelowva lu e(A )re m ain sconsta nt(C ) increa ses monotonically

(B )decreasesfi rst and the n increase s(D ) increasesfirstand thendecreases

Q .2 5 C urvaturecorrec tiontoastaf fre adingina dif fer entia llevelin gsurveyis

CE

(A)alwayssubtrac ti ve(C) alw ays addit ive

(B ) alw ay szero(D)dependent o nlati tude

5120

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2 11 CEQ 26 to Q 55 carry twom arks each

Q . 26 For a n analytic function , f x+iy)= u x,y)+iv x ,y), u is given b y u=3x /. Theexpress ion for v. c on sidering K to be a c o n stan t isA) - 3x2 + B )6x - 6y K C) 6y 6x +K D ) 6xy +

Q .27 W h a t s hould be the va lue of/. .such th at the function def ined below iscontinuou s at x=1t/2?l. .cosx if x :t: n/2f x) = x if x =n/2A) 0 B ) 2/n C) 1

Q.28 W h a t isthe va lue of the def ini te integral, j [;- ] dx?0 x+ a - xA)O B) a/2 C ) a

D ) n/2

D) 2a

Q .29 If and b are two arbitrary vectors. w ith m agnitudes a and b respectively, a X 2 w ill be e qual toB) ab - a b D ) ab a b

Q .30 The so lution of the differential equat ion dy+ 1 = x, with th econditi on that y =1 at x = 1, is x x2 XA) y=-3x - 3

X 1B ) y= -2 2x2 XC ) y =3 3

Q .3 1 Theva lue of W th at results in the coll apse of the bea m show n inthe adjoining figure and having a plastic m o me nt capaci ty ofMpi S

A) 4/21)Mp B) 3/10) Mp C ) 7/2 1) Mp

CE

2 x 2D) y=- -3x 3

Fixed w1/I

7mtl

D ) 13/2 1) Mp3m

H in g

I

612

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2011Q.32 For the cantilever bracket, PQRS, loaded as shown in the adjoining

figure PQ =RS =L and, QR =2L), which of the following statementsis FALSE

w a

A) The portion RS has a constant twisting moment with a value of2WL.B) The pottion QR has a varying twisting moment with a maximum value ofWL.C) The portion PQ has a varying bending moment with a maximum value of WL.D) The portion PQ has no twisting moment.

Q 33 Consider a bar of diameter D embedded in a largeconcrete block as shown in the adjoining figure,with a pull out force P being app lied. Let cr and 0 51be the bond strength between the bar and concrete)and the tensile strength of the bar, respectively. Ifthe block is held in position and it is assumed thatthe material of the block does not fail, which of thefollowing options represents the maximum valueofP?

pA) Maximum of : D2ab) and nDLas,)C) Minimum of : D 2a.u and nDLab)

B) Maximum of : D2as,) and nDLab)D) Minimum of : D 2a, and nDLa.w)

CE

R

Q.34 Consider two RCC beams, P and Q, each having the section 400 mm x 750 mm effective depth,d =750 mm) made with concrete having a cmax =2.1 N/mm2. For the reinforcement provided andthe grade of concrete used, it may be assumed that the c =0.75 N/mm2. The design shear in beamP is 400 kN and in beam Q is 750 kN. Considering the provisions of IS 456- 2000, which of thefollowing statements is T UA) Shear reinforcement should be designed for 175 kN for beam P and the section for beam Qshould be revised.B) Nominal shear reinforcement is required for beam P and the shear reinforcement should bedesigned for 120 kN for beam QC) Shear reinforcement should be designed for 175 kN for beam P and the shear reinforcement

should be designed for 525 kN for beam Q.D) The sections for both beams P and Q need to be revised.CE 7120

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2 11Q.35 The adjoining figure shows a schematic

representation of a steel plate girder to beused as a simply supported beam with a

CE

concentrated load. For stiffeners, PQ pi Irunning along the beam axis) and RSrunning between the top and bottom

flanges) which of the following pairs ofstatements will be TRUE? LA) i) RS shou ld be provided under the concentrated load only.

ii) PQ should be placed in the tension side of the flange.B) i) RS helps to prevent local buckling of the web.

ii) PQ should be placed in the compression side of the flange.C) i) RS should be provided at supports.

ii) PQ should be placed along the neutral axis.

+

D) i) RS should be provided away from points of action of concentrated loadsii) PQ should be provided on the compression side of the flange.Q.36 A singly under-reamed, 8-m long, RCC pile shown in the adjoining figure)

weighing 2 kN with 350 mm shaft diameter and 75 mm under-reamdiameter is installed within stiff, saturated silty clay undrained shear strengthis 5 kPa, adhesion factor is 0.3, and the applicable bearing capacity factoris 9) to counteract the impact of soil swelling on a structure constructedabove. Neglecting suction and the contribution of the under-ream to theadhesive shaft capacity, what would be the estimated ultimate tensile capacityrounded off to the nearest integer value of kN) of the pile?

A) 132 kN B) 156 kN C) 287 kN D) 301 kNQ.37 Identical surcharges are placed at ground surface at I fill Uniformsurchargesites and Y with soil conditions shown alongsideand water table at ground surface. The silty clay Water Groundlayers at and Yare identical. The thin sand layer at a b l e ~ s u r f a c e ~

Y is continuous and free-draining with a very largedischarge capacity. If p1:imary consolidation at isestimated to complete in 36 months, what would be 5mthe cotTesponding time for completion of primaryconsolidation at Y? Isotropicsaturated 10msilty clayI

' 5

Bedrock > /

L

IA) 2.25 months B) 4.5 months C) 9 months D) 36 months

CE

.____.350mm750mm

I fillWater

Isotropicsaturatedsilty clay

Thin. s a n d

layer

Isotropicsaturatedsilty clay

:; Bedrock

8120

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211 CE

Q.38 A fi eld vane sheartesting in strum ent s hown alo ngs id e) wasin sertedcomp le te ly into a depos i t ofsoft , sa turated sil ty clay w iththe vane rod vert ical such that the topofthe b ladeswere500mmbelow thegrounds urface. U ponapp li cat ion ofa rapid ly increasingtorque about the vane ro d, the soil w as found to fail w hen thetorque reached 4 .6 Nm. A ssum ing m obil izat ion of undra ined shears t rength on all fai lure swfacesto be un iform and the resista ncem obilized onth e surfa ce o f the vane rod to beneglig ible , w hatw ould bethe peakundrained shea r strength ro unded off to thenearest in teger va lu e of kPa) ofthe soil?

A)5 kPa B ) 10 kPa (C) 15 kPa

Top view pla n)

D)20 kPa

100mm

Q.3 9 A singlepipeof length 1500 m anddiameter60 emconnectstworeservoirs havinga d if ference of20m in their waterle vels. Thepipeis to be rep laced by twopipesof th e sameleng th andequald iam ete r to convey 25 m ore d ischarge under the same head loss. If the fric tion facto r isassum ed to be the same for a ll th e pipes , the valueof is app rox imately equa l to w hich ofthefollo w in goptions?A) 37.5 em B) 40.0 em (C) 45 .0 em D) 50.0 em

Q.4 0 A spi l lw ay d ischarges flood flow at a rate of 9 m 3/s per metrewidth . If the depth offlow on thehorizon tal apronat the toe ofthe spil lw ay is 46em, th e tail waterdepth needed to form a hyd rauli cjump is app ro x im atelyg iven by w hich of thefo l low ingopt ions?(A) 2.5 4 m B) 4 .9 0 m (C) 5 .7 7m D) 6.2 3m

Q.41 In an aquifer extending over150 hec tare, the watertable w as20 m below ground level. Overaperiodof ti me the water ta b le d ropped to 23 m belowthe groundle vel. I f the porosi tyof aqu ife ris0.4 0 andthe s peci f ic retentio n is0.15, w hat is the change inground waters to rageof the aquifer?A ) 67.5 ha-m B) 112 .5 ha-m (C) 180.0 ha-m D ) 450.0 ha-m

Q.42 T otal su spen ded part iculate matte r TSP) concentrati on in am bien t ai r is to be m easured using ahigh vo lum esampler. The fi l ter use d for th is purpose ha d an in itial dry weigh t of 9.7 87 g. Thefilter w as m ounted in the sampl er and the initial airflowrate through th e fil ter w as se t at1 5 m 3/m in . Sampling continued for 24hours. The a irfl owafte r 24 hours w as m easu red to be1.4 / m i n The dry w eightof the fi lter papera fter 24hour sam plingw as 10.283g. Assuming ali near decline in the air flowrateduring sampli ng ,what is the24houraverage TSP concentrat ion inthea mbi ent air?A ) 59.2 J lg/m3 C ) 237.5 J lg/m3 D ) 574.4 J lg/m3

E 9120

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2 11 CE

Q. 43 Chlori ne gas (8 mg/L as Ch) was added to a drinking wate r samp le . If the free ch lo rine residualand pH was measured to be 2 m g/L (as C l2 and 7.5, r espectively, w hat is th e concen trat ion ofresid ual OCI - io ns in the wate r? Assum e that th e c h lorine gas added to the w a te r is comp le te lycon ve rte d to HOCI and OCI-. A to mi c W e ight of Cl : 35 .5G ive n: OCl- +H + K HOCI , K = 1075(A) 1.408X 10 5 mo les/LC) 5.634 X 105 m oles /L

(B) 2.817 X 10 5 moles /L (D ) 1. 127 X 10 4 m olesfL

Q 44 I f hejamdensity isg iven askj a nd the free fl ow speed is given as u1 the m axim u mf low fo r a li neartra ffic speed-density m odel is g iven by w h ic h of the fo llowing opt ions? 3(C) - k . xu11

Q .45 If v is the i n it ial speed ofa vehicle , g is the gravita t ional acceleration, G is the upward longitudinals lope of the road and f is the coefficien t of ro lling frict ion d uri ng brak ing, the bra k in gd is tan ce(measured horiz onta lly) for the vehicl e to stop is

Q.46

CE

vA ) -g - ( -+-1,-, (B ) 2g(G+ J,

T h e cumu lative arrival and dep ar tu re curveof one cyc le o f a n approach lane of asignalized i nte rsection ts sh ow n in theadjoining figure . The cyc le timeis 50 s and theeffec tive red time is 30 s a nd th e ef fectiv egreen time is 20 s. W hat is th eavera ge delay?

(A) 15 s (B) 25 s

: I' 3 0I...0 u-:ai: ... 20' 0co Q,l 0(I I3E: Iu

10

0

C) 35 s

(D) vf(G+g

0 10 20 30 40 50Tim e s)

(D) 45 s

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201 J CEQ.47 The observ atio nsfromaclosedlooptraversearoundan obstacleareSegment Observ ation Length(m) Azimuth(clockw is efr omstati on from north)Q p M issing 33.7 500QR 300.0 00 86.3847RS R 354.524 169.3819 ST s 450.0 00 243.9 003T T 268 .000 317.5000

Whatis thevalueof th e missingmeasu rement(roundedofftoth enearest 10mm)?A) 396.8 6 m B ) 396.79m C) 396.05m D)396.94m

ommonDataQuestio nsCommonDatafo r Questions 8and49:A sandlayerfou ndatseafloorunder20mwate r depthis charac te ri zedwithrelativ edensity=40 ,maxim umvoidratio=1.0,minimumvoidra tio=0.5,andspecificgrav ityofso i lsolid s =2.67. A ssumethespecif icgrav ityofseawatertobeI .03andtheun itweigh t offreshwat ertobe9.81kN /m3.Q.48 What would beth e effectives tress (roundedofftothenearestin tegervalu eofkPa)at30mdepthintothe sandlayer?

(A )77kP a B)273kPa C)268 kPa D)28 1kPaQ.4 9 Whatwouldethechangein theeffect iv est ress(rounde dofftoth enearest in te ger va lu e ofkPa) at30 mdepthintothesa ndlayer ifth e sea water level permanentlyrisesby2m?

A) 19kPa B)0kPa C) 21 kPa D)22kP aCommonDataforQuest ions5 and51:The ordinate sofa2-hunit hydrographatl hourin te rv al s startin gfromtimet=0, are0, 3,8,6, 3,2and0m 3/s. Usetra pezoidalrule for numericalin te gration ,ifrequired.Q .50 What is the catc hmentarearepresente d bytheunit hyd rograph?

A)1.00km B )2.0 0km C)7 .92km 2 D ) 8.64km Q.51 Asto rmof6.6emoccursuniformlyoverth ecatc hment in3hours .I f j>-index isequalto 2 mrn/handbaseflowis 5m 3/s , whatisthepeakflowduetothestorm?

CEJ1120

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201 1Lin kedAnswerQuesti onsStatementforLinkedAnswe rQuestions52and53:Arig id beamis hingedatoneendandsupportedonlin earelastic sp rings(both havin gastif fn essofk)atpoints I and'2, andan in clin ed loadactsat 2,asshown.

Fixed

llinge

.

45

II~ 0 400 - - - - - - - - - - - - - - - - - - - - - - - - ~ - - - - - - - - - - ~ - - - - - - - - - - ~E.80 ))/); S {20 mm)~ 0 200.... : ::::O>ro= .c~ 0 - - - - - - - - - - - - - - - - - - - - - - ~ - - - - - - - - - - ~ - - - - - - - - ~

0.2 0.4 0.6 0.8 1Potency

Probability that microbe will overcome human immunity system)A pharmaceutical company is contemplating the development of a vaccine against the mostdangerous microbe. Which microbe should the company target in its first attempt?A) p B) Q C) R D) S

Few school curricula include a unit on bow to deal with bereavement and gr ief, and yet allstudents at some point in their lives suffer from losses through death and parting.Based on the above passage which topic would not be included in a unit on bereavement?A) how to write a letter of condolenceB) what emotional stages are passed through in the healing processC) what the leading causes of death areD) how to give support to a grieving friendA container originally contains 10 litres of pure spirit. From this container 1 litre of spirit isreplaced with 1 litre of water. Subsequently, 1 litre of the mixture is again replaced with 1 litre ofwater and this process is repeated one more time. How much spirit is now left in the container?A) 7.58litres B) 7.84 litres C) 7 litres D) 7.29 litres

A transporter receives the same number of orders each day. Currently, he has some pending ordersbacklog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can clear all theorders. Alternatively, if he uses only 3 trucks, then all the orders are cleared at the end of the lOthday. What is the minimum number of trucks required so that there will be no pending order at theend of the 5th day?A) 4 B) 5 C) 6 D) 7

Q.65 The variable cost V) of manufacturing a product varies according to the equation V= 4q , where qis the quantity produced. The fixed cost F) of production of same product reduces with q accordingto the equation F = 100/q. How many units should be produced to minimize the total cost V+F)?A) 5 B) 4 C) 7 D) 6

END OF THE QUESTION PAPERCE 14/20

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Paper Question no. Key Paper Question no. Key

CE 1 D CE 36 D

CE 2 A CE 37 C

CE 3 C CE 38 B

CE 4 B CE 39 D

CE 5 B CE 40 C

CE 6 A CE 41 B

CE 7 D CE 42 C

CE 8 C CE 43 A

CE 9 MarkstoAll CE 44 A

CE 10 B CE 45 B

CE 11 B CE 46 A

CE 12 D CE 47 B

CE 13 B/D CE 48 C

CE 14 A CE 49 B

CE 15 C CE 50 C

CE 16 A CE 51 ACE 17 D CE 52 B

CE 18 B CE 53 D

CE 19 D CE 54 C

CE 20 C CE 55 A

CE 21 A CE 56 B

CE 22 D CE 57 A

CE 23 D CE 58 D

CE 24 C CE 59 B

CE 25 A CE 60 C

CE 26 D CE 61 D

CE 27 C CE 62 C

CE 28 B CE 63 DCE 29 A CE 64 C

CE 30 D CE 65 A

CE 31 D

CE 32 B

CE 33 C

CE 34 A

CE 35 B

GATE 2011 - Answer Key - Paper : CE

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GATE Civil Engineering Solved 2011