gate civil engineering 2012

8/13/2019 GATE Civil Engineering 2012

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Q N o 1 5Carry OneMark ach

1. The estim ate of Y x obtained using S impson's rule with three-point functiono 5 X

evaluation exceeds the exact value by(A) 0. 235 (B) 0 .068 (C) 0. 024 (D ) 0 .01 2

Answer : - ( D) 1.5 1Exp:- Exact value of J dx=1.0986o5 X

Using s im pson ' sru le , in threepo int form , h = b ; a =15 ; 0 5 = 0 .5So, X 0.5 1 1.5

y 2 1 0.67

J dx = [ Yo+ Yn + 4y1 ] = = [2 +0. 7 + 4 X 3] =1 .1116t exceeds exect by =0 .012

2 The annual precipitation data of a city is normal ly distributed with mean andstandard deviat ion s 1000 mm and 200 mm, respe cti ve ly. The probabi lity tha ttheannual precip itation will be mor th an 1200 mm Is(A)


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5 The fo llowing statem ents are related to bendingof beams:I . The slope of the bending moment diagram is equal to the shear forceII. Th e slope of theshear force d iagram isequal to theload intensityI II . The slope ofthe curvatu re isequal to the flexural ro tationTV The second derivat ive of th e deflection isequal to the curvature The only FALSEstatement isA) I B) II C) III D)TV

Answer : C)dMExp: - - = V shear force)dxdvdx= w load)d2y

- 2 = v curvature )dx6. f sm a ll concrete cube is submerged deep in st i ll wter In suc h way that thepressure exerted on all faces of the cube is p, then the m ax imum shear stressde ve loped inside the cube is

A) 0A nswer: A )Exp :- l1 l1 l1 2 = P

B) 2 C) p

and t xy = 0 on ly norm a l forces ac t over it )cr cr, .so, t0 = Sin 29- t X co s29 =02crx - cr, z

( )z

mox = 2 xy = 0

D) 2p

7 As per IS 456:2000, In the im it State Designof flexura I member, the straIn inreinforc ing bars under tension at u l t imate state should not be less than) fy fy ) fy fyA E B) E 0.002 c 115E D) 1 15E 0.002

X X X X

Answ e r : D )Exp: - From IS 4 56 : 2000 )

8. Whi ch one of the fo llowing is categorised s long - term loss of pre stress inprestressedconcretem ember?A) Loss due to ela stic shortening B) Loss due to fr i c tio nC) ossdue to re laxa tion of s trands D) Loss due t o anchorage slip

A nsw e r : C)Exp: - ossd ue to re laxatio n , shr inkage, and cre ep are t ime dependent loss

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9. In ste elplate with bo lted connections, the rupture of the ne t section is modeof fa il ure underA) Te ns ion B) Compressio n C) Flexure D ) Shear

Answer: A )

10. The ratio of the theoretical critical buckling load for acolumn with fixed ends to th t of anot her column with the same dimensions and rna teriaI but with pinnedends, is equal toA) 0. 5 B) 1.0 C) 2. 0 D) 4.0

Answer : D ). ~ ~Exp : - Fo r f ixed end column, Pc = Fo r p inned end co lum n, Pc =

Hence, _s_= 4Pc

11. The effective stress fric tion angle of saturated, coheslonless soil is 38. Thera tio of shear stress to normaleffect ive stresson the failureplane isA) 0. 781 B) 0.616 C) 0. 488 D )0 .438

Ans wer : A )Exp: - C c r t a

C = o less so ilsta n 38 = 0 .781tSo, -t cr x 0 .781 = 0 .781)

12. Two series ofcompaction tests were perfo rmed in the lab oratory on an inorgan icclayey soil employing two d if ferent levels of compaction energy per unit volum eof soi l. With regard to the above tests, the fo llowing two statements are made.I. The op t imum m oisture content is expected to be more for the tests wi thhigher energyII. The max imum dry density is expected to be more for the tests w ith h igherenergyTheCORRECT option evaluating the above sta tements IsA) Only I is TRUE B) Only I I is TRUEC) Both I and I I are TRUE D) Ne i ther I nor I I Is TRUE

An swer : B)

Exp: - So, OMC Is m orefo r tes t wi th lesse r energy,Maxim um dry den sity is more for tes t withhigher energy

gh e r e nergy_/_ _ _ ~ Lesser energy~ ~

I II II I www.examrace.com


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13. As per the Indian Standard soil classification system, a sample of si l ty clay withliquid limit of 40 and plastic it y indexof 28 is classified as(A )CH (B) CI (C) CL (D) CL-ML

Answer : B)Exp:- LL = 40 and PI= 28

As pe rIS CODE ,A li ne , PI = 0 .73(LL - 20 ) = 14.6


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17. A rectangular open channelof width 5.0 m is carrying a dischargeof 100m IsThe Froude number of theflow is 0 8 Thedepth of fl ow in m) in the channel isA) 4 B) 5 C) 16 D) 20

Answer : A )Exp :- e = 100m3 Is

vB= 5m; F . = .Jgd =0.8::::> 6 = 0 .8 ::::> = 0 .8 ::::> so lv ing we get d = mvgd Bd gd

18. The circularwater pipes shown in thesketch are fl ow ing full. The velocity of f low In mls in the branch pipe R is

A) 3Answer : B )

B) 4 C) 5 D ) 6

Exp : - Using cont inuity equation ::::> Av P = Av R +(Av )Q

19. The ratio o f actual evapo-transpirat ion topotential evapo-transpiratio n is in therangeA) 0.0 to 0.4 B) 0 .6to 0.9 C) 0.0 to 1 .0 D ) 1 .0 to 2.0Answer : C)

20. A sample ofdomestic sewage is diges te d wi th si lver sulphate, sulp huric acid,potassium dischromate and mercuric sulphate in ch emical oxygendemand COD)te st. The digested sample is then t i t rated wi th standard ferrous am moniumsulphate FAS) to determ ine the un-reacted amount ofA) Mercuric sulphate B) Potassium dichromateC) Silver sulphate D )Sulphuric acid

Answer : B )21 ssertion a)

eason r)At a m anhole, the cro wn of the outgoing sewershould notbe higher than the crown of the incoming sewer.Tra nsition from a larger diam eter Incom ing sewer to asmaller diameter outgoing sewer at a manhole should notbe made .

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The CORRECT option evaluating the above statementIs:(A) Both a) and (r) are trueand (r) is thecorrect reason for a)(B ) Both (a) and (r) are true but(r ) is not the correct reason for (a)(C) Both (a ) and (r) are false(D ) (a) is t rue but (r) is false

A nswer : (A)

22. Two majorroads wi th tw o lanes each are crossing inan urban a rea to from anun-contro lled intersection. The numberof conflict points when both roads areone-way is X an dwhen both roads are two-w ay is Y . The rat io of X toY is(A) 0.25 (B ) 0 .33 C)0.50 (D )0.75

A nswer : (A)Exp: - Nu m be r of co nflictpo ints for one- way road s = 6 (x)

Nu m be rof co nflict po ints for tw o-w ay road s = 24 y)X 6So, - = - = 0 .25y 24

23. Two bitum en samples X and Y have softening points 45C and 60C,respectively. Consider the fo llowing statem ents:I. VIscosity of X will be higher than that of Y at the same temperatureII. Penetration value of X will be lesser than that of Y under standardconditions.The CORRECT option eva Iuating the above sta tements is(A) Both and I I are TRUE (B ) is F LSEand I Iis TRUE(C) Both and II areF LSE (D) is TRUE and IIF LSE

A nswer : (C )Ex p: - Lower the so ften ing , lowe r t he v iscosity 2n h ighe r t he pe net rat ion value24. Road roughness is measured using

(A ) Benklman beamC) Dynamic cone penetrometer

A nswe r : ( B)

(B) Bump integrator(D) Fal ling w eight deflectometer

25. Which of the following errors can be elim in ated by recip rocal measurements indifferential leveling?I. Error due to earth 's curvatu reII. Errordue to atmospheric-refraction(A) Both and I I (B) only (C) I I only (D) Neither nor II

A nswer : (A )www.examrace.com


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Q No. 26 5 carry Two Ma r ks Each

26 . The error in for a contin uous funct ion est imated with h = 0.03 usingdx x =xoth e central diffe re nce formula f x ) "' 0 0 ,is 2 x 10-3 TheI f(x + h) - f(x - h)dx x =xo 2hvalues of x0 and f (x 0 ) are 19.78 and 500.01 , re specti ve ly. The correspondin gerror In the central difference estimate fo rh = 0.02 is appro xi ma te ly(A) 1.3x ( B) ~ C) ( D) 9.0 x 10-4

Answer: A)27. In an exper im en t, posi t ive and negat ive va lues are equal ly l ikely to occur. Theprobabi li ty of obtaining at most one negat ive value in f ive t r ia ls is

A ) ... ._ B) ~ C) _ _ D) ~32 32 32 32Answer : D)Exp: - P = q = . .2

( 1 )0

( 1 )5

( 1 )1

( 1 )4

6robability ="Cl qn-r = 5C0 2 2 + 5C1 2 2 = 32

28. The eigen values of matrix [ ] are(A) - 2.42 and 6.86 (B ) 3.48and 13.53(C) 4 .70 and 6.86 D) 6.86 and 9.50

Answer : B)9 5 1= 0 ::::> 9 -A .)(8 - A.) =25 ::::>A.= 3. 48,13 . 535 8 - A.

29. For the paralle lo gram OPQR shown in the sketch, OP = a + b) and OR= ci +d).The area of the para llelogram is

A ) ad - beB) ac bdC) ad+ beD) b cd

Answer : A)0

Exp: - Area of para llelogram , A = OP x OR = K (ad - bc )

A= ad - be

Q

j k- --OP x O R = a b 0c d 0

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30 . The so lu tion of the o rdinary d i f fe rent ia l equation dy + 2y = 0 for the boundarydxcondltlo nr y =5 at x = 1 isA) y = zx B) y = 2e-2x C) y = 10.95e-2x D) y = 36.95e-zx

A nswer : D)Exp: - Glvenr dy 2y= 0 an d y =5 a t x = 1dx

D +2} y = 0 D = - 2 : T he so lut ion is y= C1e-2 xNowf X = 1 5= Cl e-2 5e2 = c l = 36 .95: The requI red solution is y= 3695e- 2 x

31. A s imp ly supported beam is subjec te d to a unifo rm ly d istr ibuted load of intensityw per unit length on half of the span from one end. The le ngth of the span andth e flexuralstiffness are denoted as I and EI. respecti vely. The deflection at m id -span of the beam is

5 4 5 wl4A) 6 144 I B) 768EIA nsw e r : B )

D 5 wr192 EI

32. The sketc h showsa column with a pin at theba seand rollers at thetop. t is subje c ted to an axial force P and a moment M at m id height. The reaction s) at R is/areA) A vertical force equal toPB) A vertic al force equal to P/2C) A ve rtica I force equa Ito P and a horizonta I force eq ua I to M/h D) A vert ic al force equal to P/2 and ahorizonta l fo rc eequal to M/h

A nswer : C)

33. A concrete beam prest ressed with a para bo l ic tendon is shown in the sketch. T heeccentr ic it y of the tendon is m easured from thecentroid of the cross-section. T heapplied prestressing force at service is 1620kN. The un ifo rmly distribu ted load of4 5kN/m inclu des the self-w eight

73Sectional elevation

51 1D75Cross - sec ti ontendon n o t shown

All d imens ions are in mmThe stress inN mm 2 ) in thebot tom fibre at mid-span IsA) Tension 2. 90 B) Compressive 2. 90C) Tensile 4 .32 D)Compressive 4 . 32 www.examrace.com

Answer : ( B)


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Exp: - A = 375 x 103 m m 2. . = z = bd 2 = 46875 x 103 m m 3y 6

w l2o = moment due to UDL = 299 .7 6 x 10 6 Nm m8So, stres s at bott om at m id - span = - P - Pe Mo = - 2.90N m m 2 (c ompre ss iv e}A z 2

34. A symmetric f rame PQR consists of t wo incline d m em bers PQ and QR conn ecte dat Q w ith rigid jo int, and hinged at P and R . The horizon tal length PR is I f aweight W is suspended at Q the bending moment at Q is(A) WI (B) WI (C ) WI D) Zero 2 4 8

Answer: D)

35. Two plates c onnected by fillet welds of size10 mm an d subjected to tension, as shown in the sketch. T he thickness of each plate is 12 mm. The yield stre ss andth e ultimate tensile stress ofste el are 250 MPa and 410MPa respectiv e ly. Theweld ing is done in the workshop ('Ymw = 1.25 . As per th e Limit State M ethod ofIS 800:2007, theminimum length (rounded of f to the neare st highermultiple of5 mm of each weld to transmita force Pequ al to 270kN is

(A) 100 m m Answer: B)

B) 105 m m

.. Ill150mmpC) 110 mm D) 115 m m

36. Two soli specimens with identical geometric dim ensions were subjected to fal l inghea d permeabi l i ty tests in the laboratory under identical condi t ions. The fal l ofwaterhead w as measured after an identical time In te rval . The ratio of init ial tofinal water heads for the test in vo lving the first specimen was 1 25. f thecoeff ic ient of perm eabi l i ty of the second specim en Is 5-tlmes that of the f ir st, thera tio of init ial to final water he ads in the test involving th e second specimen is(A ) 3.05 (B) 3.80 (C) 4 .00 (D) 6.25 www.examrace.com

Answer : (A )


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Exp: - For falling head tes t, In = KAth2 o1 = ek = constant[ At Jh2 {)Lst specime n, R1 = = 1.25= ekdh2

R2 = = eskd = (ek f = (RS = (1.25)5 = 3 .05

37. A layer of norm allyconsolidated, saturated silty clay of1 m thickness issubjectedto one-d imensionaI consolidation under a pressure Increm ent of 20kPa. Thepropertiesof the soil are: specific gravity= 2.7, natura l moisture content= 45 ,com pression index =0. 45, and recompression index = 0. 05. The in itia I averageeffective stress with in the layer is 100 kPa. Assuming Terzaghi's theory to beap plicable, the pr imary consolidation sett lemen t (r ounded off to the nearest mmisA) 2 mm

Answer : (D )B) 9 mm C) 14 mm D) 16 mm

38. Steady state seepage is taking place through asoil e lement at Q, 2 m below theground su rface immedia te ly downstream of the toeof n earthen dam s sh ownin the sketch. The water level ina p iezometer installed at P 500 mm above Q, isat the ground surface. The water level in a piezom eter installedat R. 500 mmbelow Q is 100 mm above the groundsurface. The bulk saturatedunitweight ofthe soil is 18 kN Im3 and the unit weigh t of water is 9.8 1 kN 3 The verticaIeff ective stress (in kPa) at Q is

(A) 14.42 (B ) 15.89 (C) 16.38 (D )18.34Answer :( B)Exp: - At P h = 1.5; R, h = 2.6; Soat Q h = 2.05

So,effective stress at e = r1 = r - u= Y - x H - Y. x h= 18 x 2 - 9.81 x 2.05 = 15.89 kNi m2

39. The top wid th and the depthof flow in a tr iangu lar ch annelwere measured s 4m and 1m, respectively. The measured velocities on the centre line at th ewatersurface. 0. 2 inand 0. 8 m below the surface are 0. 7 mls, 0. 6 mls and 0.4 mlsre spectively. Using two-po in t m ethod of velocity measurement, the d ischarge (inm 3 Is inth echannel is(A) 1.4 (B ) 1 .2 (C) 1.0 (D ) 0.8

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Answer : C )


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Exp: - As per two point m ethod of ve locity measurem entv =vo.2 vo.a = 0 .6 0.4 = o 5moan 2 2 . m sSo, Q = V x A = 0 x [ x 4 x = 1 m s

40. Group I containsparameters and GroupI I listsmethods/ins t ruments.roup I roup

P. S t ream -flow velocity 1 AnemometerQ Evapo-transpiration rate 2 Penman's methodR nfiltration rate 3 Horton's methods Wind velocity 4. C urrent meterThe CORRECT match ofGroup I with Group I I is

A) P - 1 Q 2, R 3, S - 4 B) P- 4 , Q 3, R - 2 S - 1C) P- 4 , Q - 2, R - 3, S 1

Answer : C )D) P- 1, Q 3, R - 2, 5 - 4

41 . Wheat crop re quires 55 em of water during 120 days of base period. The totalra lnfa ll dur ing th is period is 100 m m . Assumethe ir r igat ion efficiency to be 60 .Th e area (in ha) of the land which canbe irr igated with a canal f low of0 01m3 s is(A) 13.82

Answer : (A)(B) 18.85 (C) 23 .04 (D ) 230.40

42. A water sample has a pH of 9 25. Theconcentration of hydrox yl ions in the w atersample is(A) 10-9 25 moles L (B ) 10- 775 mmoles L(C) 0.302 mg/L (D ) 3.020 mg/L

A nsw e r : (C )

43. A to wn is requiredto treat 4. 2m3 min of raw water for dal ly domestic su pply.Flocculating particles are to be produced by chemical coag ulation. A columnanalysis Indicated that an over f low rateof 0.2 m m/s will produce satisfactorypartic le removal in a settl ing basin at a depthof 3.5 m. The required surface area(in m 2 ) for sett l ing is(A ) 210 (B) 350 (C) 1728 (D ) 21000

Answer :(B )Exp: - O ver flwo ra te = Q => A = g = 4 2 m3 Is = 350m2A OR 60 x 0 . 2 x 10-3 m I s

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44. A pavem ent designerhas arrived at a design trafficof 100 m II ion standard ax les


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for a newly developing nat iona l h ighway as per IRC: 37 guidelines using thefollowing data : design life =15 years, com mercial ve hic le count befo re pavementconstruction = 4500vehicles/day,annual traff ic growth rate =8 . The vehicledamage factor used in the calcula tion was(A) 1 .53 (B) 2.24 (C) 3.66 (D ) 4.14

A nswe r : (B)36SA[ (1 + t - 1]Ex p: - mSA = x VD Fr

[ (1 + 0 .08 t - 1]100 x 10 6 = 36S x 4 500 x V F VDF = 2.24r45. The following data are relatedto a horizontal curvedportion of atwo lane

highway: le ngth of curve= 200 m, radius of curv e = 300 mand width ofpavement= 7.5 m . In order to provide a stoppin gsight distance (SSD) of 80 m ,theset back dis tance (in m)required fromthe centre l ineof the inner lane of thepavement is(A ) 2.54 (B) 4.55 (C) 7 10 (D) 7 .96

An sw e r : ( B)

46. A two-lane urban road w ith one-waytraffic has a maximum capacity of 1800vehicles/h our. Under th e jam condition, the average lengthoccupied bytheve hicles is 5.0 m. The speedversus densit y relationship is linear. For a trafficvolume of 1000 vehicles/hour, the dens ity ( in vehic les/km) is(A) 52 (B) 58 (C)67 (D) 7 5

A nswer: (C)

47. The horizonta l distance between two stat ions P andQ is 100 m. The vertica langles from P and Q to the top of a vertical tower at T are 3 and so abovehorizontal, re spectively. The vertica l angles from P andQto the baseof the towerare 0.1o and0. so belowhorizonta I re spectively. Stations P, Q, andthe tower are in the sam e vertical plane with P and Q being on thesame side ofT. Neglectingearth's curvature andatmospheric refract ion, the height (in m) of the tower is(A) 6.972 (B ) 12.387 (C) 12 540 (D) 128.745

A nsw er : ( B)Ex p: - x tan 3 + tan0 .1 = ( x - 100) an 5 ta n o .s 0

228 .758He ight of tow er =228 .758 ( ta n3 + ta n 0 .1) 10 0m= 12387m X

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Common Data Questions: 48. 49


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The flow net around a sheet pile wa II is shown inth e sketch. The propertie s of thesoli are: permeabi l i ty coefficient = 0.09 m/day is o tropic), specific gravity = 2.70an d void rat io = 0.85. The sheet pile wall and the bot tom of the so il areimperm eable.

48. The seepage loss in m 3 pe r day peru nit le ngth of the wall) o f water isA) 0. 33 B) 0.38 C) 0.43 D ) 0.54

Answer : B )49. The factor of safety against the occurrence of piping failure Is

A) 3.55 B) 2.93 C) 2 .60 D ) 0 .39Answer : C)

Common Data Questions: 50 . 51

An act ivate d sludge system sketched below) is operating at equilibrium wi th thefo llowing information. W astewater related data : flow rate =500 m hau r,in f luent OD = 150 m g/L, e f f luent OD = 10 mg/L. Aerat ion tank re lated da ta :hydraulic retention time = 8 hours, m ean-cell-residen ce time = 240 hours,volume= 4000 m 3 m ixed liquor suspended solids= 2000 mg/L.

Influent ffluent

lu dge Recyde

50. The food-to-b iomass F /M) rat io inaeration tank isA) 0 .015 B) 0.210

Answer : C)

oli dsWas ted

kg OD per kg biomass per day) for theC) 0.225 D) 0 .240

Ex: - . = ..1L = 500m3 x 150mg/L = 9.375 x 10-3 k = 0 . 225 kg/dayp M t x v 200mg/L x 4000 g www.examrace.com 51. The mass in kg/day)of solids waste dfrom the sys tem Is


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A ) 2 400 0 B) 1 0 0 0 C) 800 D) 33A nsw e r : A)E xp:- Mass o f solid waste fr om syste m =200 mg x 50 0 x 103 k / hs = lO x 10 8 x 24kg da yL= 2 4 000 kg day

Lin ked Answer Quest ions: Q52to Q.SS Carry Two Marks EachStatement for inked Answer Questions: 52 53

The cro ss-sect ion at m id-span of beam at th e edge of sla b is shown in thesketc h. A por t ion of the s lab is considered as the ef fect ive f lange width for thebeam. The grades of concrete and re inforc ing steel are M25 and Fe415respective ly. The total area of reinfo rcin g bars A) is 4000 mm 2 At the u l t im a te limit state xu denotes the dep th of th e neutra l axis fr om the topfi b re. Treat thesection as under-re in forced and flanged xu> lOOmm)

52. The value of Xu in mm)computed as per the Limi t S tate Methodof IS 456:2000sA) 200.0 B ) 223 .3 C) 236 .3 D) 273.6

A nswe r : C)Exp : - 0 . 36 f bx + 0 .45fd br Dr = 0.87fyA st

0 . 36x 25 x 325 x X4 x 0 .45 x 25 x 1 000 - 3 25) x 100 = 0 .87 x 415 x 4000xu = 236 .3mm

53. The ultimate moment capaci ty in kNm) ofth e sect ion, as per the Limit Sta teM ethod of IS 456:2000 isA ) 475.2 B) 717.0 C) 756.4 D) 762.5

An swe r : B)Statementfo r inked Answer Quest ions :54 55

Th e drainage area of watershed is 50 km The Index is 0.5 em/hour and thebase flo wat the outlet is 10m3 Is One hour unit hydrograph un it depth= 1 em) ofthe watershed is tr ia ngular in shape with tim e base of 15 hours. The peakord in a te occurs at 5 hours.

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54. Thepeak ordinate(in m 3 I s I em) of the unit hydrograph Is


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(A) 10.00 (B) 18.52 (C) 37.03 D) 185.20A nswe r : B)Ex p - . . x Bx H = A rea x (1cm ra in f a 11

1> x 1S x 3600 x H = 50 x 106 x 0 .01 > H =18 .52m 3 s.cm

55. For a storm of depth of 5.5 em and durat ion of 1 hour, the peak ord inate(in m 3 /s ) o the hydrograph is(A) 55.00 ( B) 82.60 C) 92.60 (D ) 102.60

Answer : (C)Exp: - Runoff = Ral nfaii = 5.5 0. S = Sc m

Peak o Hyd rog rap h = Peak of uni t Hydrog raph x Scmm 3 s= 18.52 - - x Scm = 18.52m3 /secem

Q No. 56 60Carry One MarkEach56. Choose the most appropr iate alternative from the opt ions given below tocom plete the fol low ing sentence:

Despite several the mis s ion s uc c e e d ed in its attempt toresolve the c on fl ict .(A) attempts (B) setbacks (C) m eet ings D) delegat ions

Answer : B)

57. T he cost funct ion for a product in afirm is given by 5 q = 5 unitsdq

58. Choose the most appropr iate alternative f rom the op t ions given below tocomple te the fo l lowing sentence:Suresh s dog is the one was hurt in the stampede.(A ) that (B) which (C ) who D) whom 59.

Answer : (A)www.examrace.com

59. Choose th grammat ica lly INCORRECT sentence:


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(A) They gave us th money back less the se r vice charges of Th ree Hundredrupees.(B) This country s expenditure is not less than that of Bangladesh.(C)The com m ittee in i t ia lly asked for a funding of F if ty Lakh rupeesr but la te rsettled for a lessersum.(D) This country s expend it ure on educational reform s Is very less

A nswe r : (D )

60. Which o ne of the follow ing opt ions is the closest in meaning to the word giv enbelow?Mitigate(A) Diminish (B) Divulge (C) Dedicate (D) Denote

A nsw e r : (A)

Q No . 6 65 Carry Two Marks Each

61. A political party orders an arch forth entrance to the gro und in which the annualconve ntion isb eing held. The profile of the arch follows the equation y = 2x 0.1x where y is the height of the arch inmeters . The m ax imum poss ible height of thearch is (A) 8 m eters (B) 10 meters (C) 12 mete rs (D ) 14 meters

A nsw e r : (B)x p : y = 2x - 0.1x 2

dydx = 2 - 0 .2x

< 0 : y ma x imises at 2 - 0 .2x=O10

: y = 20 - 10 = 10 m

62. Wanted Tem porary/ Part- t im e persons for th post of Field Interviewer to conduct persona l interv iews to collect and collate economic data. Requirements: HighSch oo l-passr must be available for ayr vening an d Saturday work.Transportatio n paidr expense s reimbursed.Which one of th following is th best inference from th e above advertis ement?(A) Gender-discrimina tory(B) Xenophobic(C) Not design ed to rna kethe post attrac t ive(D ) Not gender-d is cr iminatory

A nswer : C)www.examrace.com


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63. Given the sequence of terms, AD CG FK JP, the next term is(A) OV (B) OW C) PV (D) PW

Answer: (A) 1 2 ~ 4Exp:- I I I I D CG FK J p ovI I I I t2 3 ~ 564. Which of the following assertions are CORRECT?

P: Adding 7 to each entry in a list adds 7 to the mean of the listQ: Adding 7 to each entry in a list adds 7 to the standard deviation of the listR: Doubling each entry in a list doubles the mean of the I stS: Doubling each entry in a I st leaves the standard deviation of the l is t unchanged(A) P, Q (B) Q, R C) P, R (D) R, S

Answer: C)Ex p: - (P) Consider the exam pie,

1+ 2 + 3+4Let entry be 1, 2,3, 4; So, mean = = 2. 54Add 7 to all entry8, 9, 10,11

M_ 8 + 9+ 10 + 11 _ 9 5 - 2 5 (7)e - - . - . +4(R) Double the entry,2, 4,6,8

2+ 4 + 6 + 8Mea n = = 5 = 2x 2.5465. An automobile plant contracted to buy shock absorbers from two suppliers X andY.X supplies 60 andY supplies 40 of the shock absorbers. All shock absorbers are

subjected to a quality test. The ones that pass the quality test are considered reliableOf X s shock absorbers, 96 are reliable. Of Y s shock absorbers, 72 are reliable.The probability that a randomly chosen shock absorber, which is found to be reliable,is made by Y is(A) 0.288 (B) 0.334 C) 0.667 (D) 0.720

Answer : (B)Exp:-

SupplyRel iable

X6096

4072

Overall 0.576 0.2880.288

: P(x )= 0.576 + 0.288 = 0334www.examrace.com

gate civil engineering 2012

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