civil engineering gate previous papers 2012-2000

ACE ENGINEERING ACADEMYHYDERABAD, A.P. Phones : 040-24752469, 24750437

GATE – 2011 * KEY SHEET

CE : CIVIL ENGINEERING

Q.No. Answer

23 D

24 C

25 A

26 D

27 C

28 B

29 A

30 D

31 D

32 B

33 C

34 A

35 B

36 C

37 C

38 B

39 D

40 C

41 B

42 C

43 B

44 A

Q.No. Answer45 B46 A47 B48 D49 B

50 C51 A52 B53 D54 C55 A56 B57 A58 D59 D60 C61 D62 C63 D64 C65 A

Q.No. Answer

1 D

2 A

3 C

4 B

5 B

6 C

7 A

8 C

9 A

10 B

11 B

12 D

13 B

14 A

15 C

16 A

17 D

18 B

19 D

20 C

21 A

22

NOTES :

1. Utmost care is taken while preparing the above key. Discrepancies, if any, may please be brought to our notice.

2. Please contact us immediately after GATE result, for M.Tech counseling details and suggestions.

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Q. No. 1 – 25 Carry One Mark Each

1. x 0

2sin x3

The lim isx

(A) 23 (B) 1 (C) 1

4 (D) 12

2. Two coins are simultaneously tossed. The probability of two heads simultaneously appearing is

(A) 18 (B) 1

6 (C) 14 (D) 12

3. The order and degree of the differential equation

33

23

d y dy4 y 0 are respectively

dxdx

(A) 3 and 2 (B) 2 and 3 (C) 3 and 3 (D) 3 and 1

5. For the truss shown in the figure, the force in the member QR is

(A) Zero (B) P2

(C) P (D) 2 P

6. The major and minor principal stresses at a point are 3MPa and -3MPa respectively. The maximum shear stress at the point is

(A) Zero (B) 3MPa (C) 6MPa (D) 9MPa

Q

T

LS

R

L

P

4. Two people weighing W each are sitting on a plank of length L floating on water

at from either end. Neglecting the weight of the plank, the bending moment L4

at the centre of the plank is

(A) WL

8 (B)

WL16

(C) (D) zero WL32

7. The number of independent elastic constants for a linear elastic isotropic and homogeneous material is

(A) 4 (B) 3 (C) 2 (D) 1

8. The effective length of a column of length L fixed against rotation and translation at one end and free at the other end is

(A) 0.5 L (B) 0.7 L (C) 1.414 L (D) 2L

9. As per India standard code of practice for pre stressed concrete (IS:1343-1980) the minimum grades of concrete to be used for post-tensioned and pre-tensioned structural elements are respectively

(A) M20 for both (B) M40 and M30 (C) M15 and M20 (D) M30 and M40

10. A solid circular shaft of diameter d and length L is fixed at one end and free at the other end. A torque t is applied at the free end. The shear modulus of the material is G. The angle of twist at three free ends is

(A) 4

16TLd G

(B) 4

32TLd G

(C) 4

64TLd G

(D) 4

128TLd G

11. In a compaction test, G, w, S and e represent the specific gravity, water content,

degree of saturation and void ratio of the soil sample, respectively. If w

represents the unit weight of water and w represents the dry unit weight of the soil, the equation for zero air voids line is

(A) wd

G1 Se

(B) wd

G1 Gw

(C) wd

w

Ge S

(D) d

Gw1 Se

12. A fine grained soil has liquid limit of 60 and plastic limit of 20. As per the plasticity chart, according to IS classification, the soil is represented by the letter symbols

(A) CL (B) CI (C) CH (D) CL-ML

13. Quick sand condition occurs when

(A) The void ratio of the soil becomes 1.0

(B) The upward seepage pressure in soil becomes zero

(C) The upward seepage pressure in soil becomes equal to the saturated unit weight of the soil

(D) The upward seepage pressure in soil becomes equal to the submerged unit weight of the soil

CE GATE 2010

14. The e-log p curve shown in the figure is representative of

(A) Normally consolidated clay

(B) Over consolidated clay

(C) Under consolidated clay

(D) Normally consolidated clayey sand

15. If h v h v, , , and represent the total horizontal stress, total vertical stress, effective horizontal stress and effective vertical stress on a soil element, respectively, the coefficient of earth pressure at rest is given by

(A) h

v

(B) h

v' (C) v

h

(D) v

h'

16. A mild-sloped channel is followed by a steep-sloped channel. The profiles of gradually varied flow in the channel are

(A) 3 2M ,S (B) 3 3M ,S (C) 2 1M ,S (D) 2 2M ,S

17. The flow in a rectangular channel is subcritical. If width of the channel is reduced at a certain section, the water surface under no-choke condition will

(A) Drop at a downstream section (B) Rise at a downstream section

(C) Rise at an downstream section (D) Not undergo any change

18. The correct match of Group-I with Group-II is

Group-II Group-II

P. Evapotranspiration 1. Penman method

Q. Infiltration 2. Snyder’s method

R. Synthetic unit hydrograph 3. Muskingum method

S. Channel Routing 4. Horton’s method

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

(C) P-3, Q-4, R-1, S-2 (D) P-4, Q-2, R-1, S-3

19. Group-I gives a list of devices and Group-II gives the list of uses

P. Pitot tube 1. Measuring pressure in a pipe

Q. Manometer 2. Measuring velocity of flow in a pipe

R. Venturimeter 3. Measuring air and gas velocity

S. Anemometer 4. Measuring discharge in a pipe

logp

CE GATE 2010

The correct match of Group-I with Group-II is

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

(C) P-2, Q-1, R-4, S-3 (D) P-4, Q-1, R-3, S-2

20. A coastal city produces municipal solid waste (MSW) with high moisture content, high organic materials, low calorific value and low inorganic materials. The most effective and sustainable option for MSW management in that city is

(A) Composting (B) Dumping in sea (C) Incineration (D) Landfill

21. According to the Noise Pollution (Regulation and control) Rules, 2000, of the Ministry of Environment and Forests, India, the day time and night time noise level limits in ambient air for residential areas expressed in dB(A) Leg are

(A) 50 and 40 (B) 55 and 45 (C) 65 and 55 (D) 75 and 70

22. An air parcel having 40ºC temperature moves from ground level to 500m elevation in dry air following the “adiabatic lapse rate”. The resulting temperature of air parcel at 500m elevation will be

(A) 35ºC (B) 38ºC (C) 41ºC (D) 44ºC

23. Aggregate impact value indicates the following property of aggregates

(A) Durability (B) Toughness (C) Hardness (D) Strength

24. As per IRC: 67-2001, a traffic sign indicating the Speed Limit on a road should be of

(A) Circular Shape with White Background and Red Border

(B) Triangular Shape with White Background and Red Border

(C) Triangular Shape with Red Background and White Border

(D) Circular Shape with Red Background ad White Border

25. The local mean time at a place located in longitude 90º 40’E when the standard time is 6 hours and 30 minutes and the standard meridian is 82º 30’E is

(A) 5 hours, 2 minutes and 40 seconds

(B) 5 hours, 57 minutes and 20 seconds

(C) 6 hours, and 30 minutes

(D) 7 hours, 02 minutes and 40 seconds

CECECE GGGATEATEATE 201020102010

Q. No. 26 – 51 Carry Two Marks Each

26. The solution to the ordinary differential equation 2

2

d y dy6y 0 is

dxdx

(A) 3x 2x1 2y c e c e (B) 3x 2x

1 2y c e c e

(C) 3x 2x1 2y c e c e (D) 3x 2x

1 2y c e c e

27. The inverse of the matrix 3 2i i

isi 3 2i

(A) 3 2i i1

12 i 3 2i (B)

3 2i i112 i 3 2i

(C) 3 2i i1

14 i 3 2i (D)

3 2i i114 i 3 2i

28. The table below gives values of a function F(x) obtained for values of x at intervals of 0.25.

x 0 0.25 0.5 0.75 1.0

F(x) 1 0.9412 0.8 0.64 0.50

The value of the integral of the function between the limits 0 to 1 using Simpson’s rule is

(A) 0.7854 (B) 2.3562 (C) 3.1416 (D) 7.5000

29. The partial differential equation that can be formed from

z zz ax by ab has the form with p and q

x y

(A) z=px+qy (B) z=px+pq (C) z=px+qy+pq (D) z=qy+pq

30. A parabolic cable is held between two supports at the same level. They horizontal

span between the supports is L. The sag at the mid-span is h. The equation of

the parabola is 2

2

xy 4h ,

L where x is the horizontal coordinate and y is the

vertical coordinate with the origin at the centre of the cable. The expression for the total length of the cable is

(A) L 2 2

40

h x1 64 dx

L (B)

L /2 3 2

40

h x2 1 64 dx

L

(C) L /2 2 2

40

h x1 64 dx

L (D)

L /2 2 2

40

h x2 1 64 dx

L


31. Given a function

2 2f x,y 4x 6y 8x 4y 8

The optimal value of f(x, y)

(A) Is a minimum equal to 10/3 (B) Is a maximum equal to 10/3

(C) Is a minimum equal to 8/3 (D) Is a maximum equal to 8/3

32. A double cover butt riveted joint is used to connect two flat plates of 200mm width and 14mm thickness as show in the figure. There are twelve power driven rivets of 20mm diameter at a pitch of 50mm in both directions on either side of the plate. Two cover plates of 10mm thickness are used. The capacity of the joint in tension considering bearing and shear ONLY, with permissible bearing and shear stresses as 300MPa respectively is

(A) 1083.6kN (B) 871.32kN (C) 541.18kN (D) 433.7kN

33. Two plates, subjected to direct tension, each of 10mm thickness and having

widths of 100mm and 175mm, respectively are to be fillet welded with an overlap of 200mm. Given that the permissible weld stress is 110MPa and the permissible stress in steel is 150MPa, then length of the weld required using the maximum permissible weld size as per IS: 800-1984 is

(A) 245.3mm (B) 229.2mm (C) 205.5mm (D) 194.8mm

50mm

50mm

50mm

50mm

50mm 50mm 50mm

100mm 175mm

200mm


34. For the simply supported beam of length L, subjected to a uniformly distributed moment M kN-m per unit length as shown in the figure, the bending moment (in kN-m) at the mid-span of the beam is

(A) Zero (B) M (C) ML (D) M/L

35. A disc of radius r has a hole of radius r2 cut-out as shown. The centroid of the

remaining disc (shaded portion) at a radial distance from the centre “O” is

(A) r2

(B) r3

(C) r6

(D) r8

36. A three hinged parabolic arch having a span of 20m and a rise of 5m carries a point load of 10kN at quarter span from the left end as shown in the figure. The resultant reaction at the left support and its inclination with the horizontal are respectively

(A) 9.01kN and 56.31º (B) 9.01kN and 33.69º

(C) 7.50kN and 56.31º (D) 2.50kN and 33.69º

L

M kN - m per unit length

r /2

'O'

O

r

5m 5m 10m

5m

10kN


37. The vertical stress at point P1 due to the point load Q on the ground surface as shown in figure is s2. According to Boussinesq’s equation, the vertical stress at point P2 shown in figure will be

(A) z

2 (B) z (C) z2 (D) z4

38. An open ended steel barrel of 1m height and 1m diameter is filled with saturated

fine sand having coefficient of permeability of 210 m / s . The barrel stands on a

saturated bed of gravel. The time required for the water level in the barrel to drop by 0.75m is

(A) 58.9s (B) 75s (C) 100s (D)150s

39. The ultimate load capacity of a 10m long concrete pile of square cross section 500mm x 500mm driven into a homogeneous clay layer having undrained cohesion value of 40kPa is 700kN. If the cross section of the pile is reduced to 250mm x 250mm and the length of the pile is increased to 20m, the ultimate load capacity will be

(A) 350kN (B) 632.5kN (C) 722.5kN (D) 1400kN

40. For a rectangular channel section, Group I lists geometrical elements and Group II gives proportions for hydraulically efficient section.

Group I Group II

P Top width 1 ey2

Q Perimeter 2 ey

R Hydraulic Radius 3 2 ey

S Hydraulic Depth 4 4 ey

ye is the follow depth corresponding to hydraulically efficient section. The correct match of Group I with Group II is

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

(C) P-3,Q-4,R-1,S-2 (D) P-3,Q-4,R-2,S-1

Q

z2

2Pr2

1P

z

r


41. The Froude number of flown in a rectangular channel is 0.8. If the depth of flow is 1.5m, the critical depth is

(A) 1.80m (B) 1.56m (C) 1.36m (D) 1.29m

42. A wall of diameter 20cm fully penetrates a confined aquifer. After a long period of pumping at a rate of 2720litres per minute, the observations of drawdown taken at 10m and 100m distances from the center of the wall are found to be 3m and 0.5m respectively. The transmissivity of the aquifer is

(A) 676m2/day (B) 576 m2/day (C) 526 m2/day (D) 249 m2/day

43. If the BOD3 of a wastewater sample is 75mg/L and reaction rate constant k

(base e) is 0.345 per day, the amount of BOD remaining in the given sample after 10days is

(A) 3.21 mg/L (B) 3.45 mg/L (C) 3.69 mg/L (D) 3.92 mg/L

44. Consider the following statements in the context of geometric design of roads.

I: A simple parabolic curve is an acceptable shape for summit curves.

II: Comfort to passengers is an important consideration in the design of summit curves.

The correct option evaluating the above statements and their relationship is

(A) I is true, II is false

(B) I is true, II is true, and II is the correct reason for I

(C) I is true, II is true, and II is NOT the correct reason for I

(D) I is false, II is true

45. The design speed for a two-lane road is 80kmph. When a design vehicle with a wheelbase of 6.6m is negotiating a horizontal curve on that road, the off-tracking is measured as 0.096m. The required widening of carriageway of the two-lane road on the curve is approximately

(A) 0.55m (B) 0.65m (C) 0.75m (D) 0.85m

46. Consider the following statements in the context of cement concrete pavements.

I. Warping stresses in cement concrete pavements are caused by the seasonal variation in temperature.

II. Tie bars are generally provided across transverse joints of cement concrete pavements

The correct option evaluating the above statements is

(A) I: True II: False (B) I: False II: True

(C) I: True II: True (D) I: False II: False

47. A bench mark has been established at the soffit of an ornamental arch at the known elevation of 100.0m above sea level. The back sight used to establish height of instrument is an inverted staff reading of 2.105m. A forward sight reading with normally held staff of 1.105m is taken on a recently constructed plinth. The elevation of the plinth is

(A) 103.210m (B) 101.000m (C) 99.000m (D) 96.790m

Common Data Questions: 48 & 49

Ion concentrations obtained for a groundwater sample (having pH=8.1) are given below.

Ion Ca2+ Mg2+ Na+ HCO3- SO4

2- Cl-

Ion concentration (mg/L)

100 6 15 250 45 39

Atomic Weight Ca=40 Mg=24 Na=23 H=1, C=12, O=16

S=32, O=16

Cl=35.5

48. Total hardiness (mg/L as CaCO3) present in the above water sample is

(A) 205 (B) 250 (C) 275 (D) 308

49. Carbonate hardness (mg/L as CaCO3) present in the above water sample is

(A) 205 (B) 250 (C) 275 (D) 289


The moisture holding capacity of the soil in a 100 hectare farm is 18cm/m. the field is to be irrigated when 50 percent of the available moisture in the root zone is depleted. The irrigation water is to be supplied by a pump working for 10hours a day, and water application efficiency is 75%. Details of crops planned for cultivation are as follows:

Crop Root zone depth (m) Peak rate of moisture use

(mm/day)

X 1.0 5.0

Y 0.8 4.0

50. The capacity of irrigation system required to irrigate crop X in 36 hectares is

(A) 83litres/sec (B) 67 liters/sec (C) 57 liters/sec (D) 53 liters/sec


51. The area of crop Y that can be irrigated when the available capacity of irrigation system is 40 liters / sec is

(A) 40hectares (B) 36 hectares (C) 30 hectares (D) 27 hectares

Linked Answer Questions 52 & 53

A doubly reinforced rectangular concrete beam has a width of 300mm and an effective depth of 500mm. the beam is reinforced with 2200mm2 of steel in tension and 628mm2 of steel in compression. The effective cover for compression steel is 50mm. Assume that both tension and compression steel yield. The grades of concrete and steel used are M20 and Fe250 respectively. The stress lock parameters (rounded off to first two decimal places) for concrete shall be as per IS 456:200.

52. The depth of neutral axis is

(A) 205.30mm (B) 184.56mm (C) 160.91mm (D) 145.30mm

53. The moment of resistance of the section is

(A) 206.00kN-m (B) 209.20 kN-m (C) 236.80 kN-m (D) 251.90kN-m,

Statement for Linked Answer Questions: 54 & 55

The unconfined compressive strength of a saturated clay sample is 54kPa.

54. The value of cohesion for the clay is

(A) zero (B) 13.5kPa (C) 27kPa (D)54kPa

55. If a square footing of size 4m x 4m is resting on the surface of a deposit of the

above clay, the ultimate bearing capacity of the footing (as per Terzaghi’s equation) is

(A) 1600kPa (B) 315kPa (C) 27kPa (D)54kPh

Q. No. 56 – 60 Carry One Mark Each

56. Which of the following options is closest in meaning to the word Circuitous.

(A) cyclic (B) indirect (C) confusing (D) crooked

57. The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair.

Unemployed: Worker

(A) fallow: land (B) unaware: sleeper

(C) wit: jester (D) renovated: house


58. Choose the most appropriate word from the options given below to complete the following sentence:

If we manage to ____________ our natural resources, we would leave a better planet for our children.

(A) uphold (B) restrain (C) cherish (D) conserve

59. Choose the most appropriate word from the options given below to the complete the following sentence:

His rather casual remarks on politics ___________ his lack of seriousness about the subject.

(A) masked (B) belied (C) betrayed (D)suppressed

60. 25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is:

(A) 2 (B)17 (C)13 (D) 3

Q. No. 61 – 65 Carry Two Marks Each

61. Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters).

All were born on 1st January. The age difference between any two successive siblings (that is born one after another) is less than 3 years. Given the following facts:

i. Hari’s age + Gita’s age > Irfan’s age + Saira’s age

ii. The age difference between Gita and Saira is 1 year. However Gita is not the oldest and Saira is not the youngest.

iii. There are no twins.

In what order were they born (oldest first)?

(A) HSIG (B) SGHI (C) IGSH (D) IHSG

62. 5 skilled workers can build a wall in 20days: 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?

(A) 20 (B) 18 (C) 16 (D) 15

63. Modern warfare has changed from large scale clashes of armies to suppression of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare; and regretfully, there exist people in military establishments who think that chemical agents are useful tools for their cause.


Which of the following statements best sums up the meaning of the above passage:

(A) Modern warfare has resulted in civil strife.

(B) Chemical agents are useful in modern warfare.

(C) Use of chemical agents in warfare would be undesirable

(D) People in military establishments like to use chemical agents in war.

64. Given digits 2,2,3,3,4,4,4,4 how many distinct 4 digit numbers greater than 3000 can be formed?

(A) 50 (B) 51 (C) 52 (D) 54

65. If 137+276=435 how much is 731+672?

(A) 534 (B) 1403 (C) 1623 (D)1513


v=v ln k / kfj , where v and kfj are the free flow speed and jam densityrespectively. When the highway is operating at capacity, the density obtained asper this model is(A) e.kj (B) kj (C) k / 2j (D) k / ej

48. A three-phase traffic signal at an intersection is designed for flows shown in thefigure below. There are six groups of flows identified by the numbers 1 through6. Among these 1, 3, 4 and 6 are through flows and, 2 and 5 are right turning.Which phasing scheme is not feasible?

5 4

6

3

1 2

Combination choice Phase I Phase II Phase III

(A) P

P

Q

R

S

(B) Q

1, 4

1, 2

2, 5

1, 4

2, 5

4, 5

1, 3

2, 6

(C) R

3, 6

3, 6

4, 6

3, 5

(D) S

49. The magnetic bearing of a line AB was N 59º 30’ W in the year 1967, when thedeclination was 4º 10’ E. If the present declination is 3ºW, the whole circlebearing of the line is(A) 299º 20’ (B) 307º 40’ (C) 293º 20’ (D) 301º 40’

CE

50. Determine the correctness or otherwise of the following Assertion [a] and theReason [r] :Assertion [a] : Curvature correction must be applied when the sights are longReason [r] : Line of collimation is not a level line but is tangential to the levelline(A) Both [a] and [r] are true and [r] is the correct 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 false but [r] is true


Examine the test arrangement and the soil properties given below

5m

Concrete block1.5 1.0 0.6m high

Saturated dense sand

5m

Rigid Steel Beam

G.W.T.

500mm diameter bored pile3

18kN / msat

35º , c 0 kPa5m Angle of friction 24º

N 403

Earth pressure coefficient K 1.5

w 10kN / m

51. The maximum pressure that can be applied with a factor of safety of 3 throughthe concrete block, ensuring no bearing capacity failure in soil using Terzaghi’sbearing capacity equation without considering the shape factor, depth factor andinclination factor is(A) 26.67kPa (B) 60kPa (C) 90kPa (D) 120kPa

52. The maximum resistance offered by the soil through skin friction while pulling outthe pile from the ground is(A) 104.9kN (B) 209.8kN (C) 236kN (D) 472kN

CE


Following chemical species were reported for water sample from a well:SpecialsChloride (Cl-)Sulphate (SO4

2-)Carbonate (CO3

2-)Bicarbonate (HCO3

-)Calcium (Ca2+)Magnesium (Mg2+)pH

Concentration (milli equivalent/L)1515053012188.5

53. Total hardness in mg/L as CaCO3 is(A) 1500 (B) 2000 (C) 3000 (D) 5000

54. Alkalinity present in the water in mg/L as CaCO3 is(A) 250 (B) 1500 (C) 1750


(D) 5000

One hour triangular unit hydrograph of a watershed has the peak discharge of60m3/sec.cm at 10hours and time base of 30 hours. The index is 0.4cm perhour and base flow is 15m3m/sec

55. The catchment area of the watershed is(A) 3.24km2 (B) 32.4km2 (C) 324km2 (D) 3240km2

56. If these is rainfall of 5.4cm in 1 hour, the ordinate of the flood hydrograph at 15th

hour is(A) 225 m3/sec (B) 240 m3/sec (C) 249 m3/sec (D) 258 m3/sec

Linked Answer Questions: Q.57 to Q.60 Carry Two Marks Each


In the cantilever beam PQR shown in figure below, the segment PQ has flexuralrigidity EI and the segment QR has infinite flexural rigidity

W

PEl

L

Q Rigid

L

R

CE

57. The deflection and slope of the beam at ‘Q’ are respectively3 2 3 2 3 2 3 2

(A) 5WL6EI

and 3WL2EI

(B) WL3EI

and WL2EI

(C) WL2EI

and WLEI

WL (D)

3EIand 3WL

2EI

58. The deflection of the beam at ‘R’ is8WL35WL3 7WL3 8WL3

(A) EI (B) 6EI (C) 3EI (D) 6EI


59. A saturated undisturbed sample from a clay strata has moisture content of3

22.22% and specific weight of 2.7. Assuming w10kN / m , the void ratio andthe saturated unit weight of the clay, respectively are

3 3(A) 0.6 and 16.875kN / m

3

(B) 0.3 and 20.625 kN / m3

(C) 0.6 and 20.625kN / m (D) 0.3 and 16.975 kN / m

60. Using the properties of the clay layer derived from the above question, theconsolidation settlement of the same clay layer under a square footing(neglecting its self weight) with additional data shown in the figure below(assume the stress distribution as 1H:2V from the edge of the footing and

3

w10kN / m ) is

1.0m

200kN

G.W.T.Saturated sand

318kN / m

1.0m

1.0m

2m 2m1 2

sat

Stiff ClayC

(A) 32.78mm (B) 61.75mm

Compression Index C 0.4Dense sand

(C) 79.5mm (D) 131.13mm

1 1 is

(A) 0.247 (B) 2.473

4

3(C) 24.7

5

(D) 247

Q.26 The Eigen values of the matrix are

(A) -7 and 82 5

(B) -6 and 5 (C) 3 and 4 (D) 1 and 2

Q.27 A person on a trip has a choice between private car and public transport. Theprobability of using a private car is 0.45. While using the public transport, furtherchoices available are bus and metro, out of which the probability of commutingby a bus is 0.55. In such a situation, the probability (rounded up to two decimals)of using a car, bus and metro, respectively would be

(A) 0.45, 0.30 and 0.25(C) 0.45, 0.55 and 0.00

(B) 0.45, 0.25 and 0.30(D) 0.45, 0.35 and 0.20

Q.28 The following simultaneous equationsx+y+z=3x+2y+3z=4x+4y+kz=6will NOT have a unique solution for k equal to(A) 0 (B) 30 (C) 6

uv uv

(D) 7

Q.29 The inner (dot) product of two vectors and is zero. The angle (degrees)between the two vectors is(A) 0 (B) 5 (C) 90 (D) 120

Q.30 Cross-section of a column consisting of two steel strips, each of thickness t and widthb is shown in the figure below. The critical loads of the column with perfect bond andwithout bond between the strips are P and P0 respectively. The ration P/Po is(A) 2 (B) 4 (C) 6 (D) 8

4

CE Civil Engineering: Gate 2008 Paper

Q.31 A rigid bar GH of length L is supported by a hinge and a spring of stiffness K asshown in the figure below. The buckling load, Pcr’ for the bar will be

(A) 0.5 KL

(B) 0.8 KL

(C) 1.0KL

(D) 1.2KL

Q.32 The degree of static indeterminacy of the rigid frame having two internal hingesas shown in the figure below, is

(A) 8

(B) 7

(C) 6

(D) 5

Q.33 The members EJ and IJ of a steel truss shown in the figure below are subjected toa temperature rise of 300C. The coefficient of thermal expansion of steel is0.000012 per 0C per unit length. The displacement (mm) of joint E relative tojoint H along the direction HE of truss, is

(A) 0.255

(B) 0.589

(C) 0.764

(D) 1.026

Q.34 The maximum shear stress in a solid shaft of circular cross-section havingdiameter subjected to a torque T is . If the torque is increased by four times andthe diameter of the shaft is increased by two times, the maximum shear stress inthe shaft will be

5

(A) 2


(B) (C) /2 (D) /4

Q.35 The span(s) to be loaded uniformly for maximum positive (upward) reaction atsupport P, as shown in the figure below, is (are)

(A) PQ only (B) PQ and QR (C) QR and RS (D) PQ and RS

Q.36 A vertical PQ of length L is fixed at its top end P and has a flange to the bottomend Q. A weight W is dropped vertically from a height h (<L) on to the flange.The axial stress in the rod can be reduced by

(A) increasing the length of the rod(B) decreasing the length of the rod(C) decreasing the area of cross-section of the rod(D) increasing the modulus of elasticity of the material

Q.37 Un-factored maximum bending moments at a section of a reinforced concretebeam resulting from a frame analysis are 50, 80, 120 and 180kNm under dead,live, wind and earthquake loads respectively. The design moment (kNm) as perIS: 456- 2000 for the limit state of collapse (flexure) is

(A) 195 (B) 250 (C) 345 (D) 372

Q.38 A reinforced concrete column contains longitudinal steel equal to 1 percent of netcross-sectional area of the column. Assume modular ration as 10. the loads carried(using the elastic theory) by the longitudinal steel and the net area of concrete, arePs and Pc respectively. The ration Ps/Pc expressed as percent is

(A) 0.1 (B) 1 (C) 1.1 (D) 10

Q.39 A pre-tensioned concrete member of section 200mm x 250mm contains tendonsof area 500 mm2 at the centre of gravity of the section. The pre-stress in tendonsis 1000N/mm2. Assuming modular ratio as 10, the stress (N/mm2) in concrete is

(A) 11 (B) 9 (C) 7 (D) 5

6


Q.40 Rivets and bolts subjected to both shear stress ( vf, cal) and axial tensile stress( tf,cal) shall be so proportioned that the stresses do not exceed the respective

allowable stresses vf and tf, and the

value of

,,

does not exceed

(A) 1.0 (B) 1.2 (C) 1.4 (D) 1.8

Q.41 A continuous beam is loaded as shown in the figure below. Assuming a plasticmoment capacity equal to MP, the minimum load at which the beam wouldcollapse is

( ) 4 ( ) 6 ( ) 8 ( ) 10

Q.42 The maximum tensile stress at the section X-X shown in the figure below is

( ) 8 ( ) 6 ( ) 4 ( ) 2

Q.43 The stepped cantilever is subjected to movements, M as shown in the figurebelow. The vertical deflection at the free end (neglecting the self weight) is

2

(A)8

2

(B)4

2

(C)2

(D) Zero


Q.44 The liquid limit (LL), plastic limit (PL) and shrinkage limit (SL) of a cohesivesoil satisfy the relation(A) LL>PL<SL (B) LL>PL>SL (C) LL<PL<SL (D) LL<PL>SL

Q.45 A footing 2m x 1m exerts a uniform pressure of 150kN/mm2 on the soil.Assuming a load dispersion of 2 vertical to 1 horizontal, the average verticalstress (kN/m2) at 1.0m below the footing is(A) 50 (B) 75 (C) 80 (D) 100

Q.46 A direct shear test was conducted on a cohesion-less soil (c=0) specimen under anormal stress of 200kN/m2. The specimen failed at a shear stress of 100kN/m2.The angle of internal friction of the soil (degrees) is(A) 26.6 (B) 29.5 (C) 30.0 (D) 32.6

Q.47 A pile of 0.50m diameter and length 10m is embedded in a deposit of clay. Theundrained strength parameters of the clay are cohesion = 60kN/m2 and the anglein internal friction = 0. The skin friction capacity (kN) of the pile for an adhesionfactor of 0.6, is(A) 671 (B) 565 (C) 283 (D) 106

Q.48 A saturated clay stratum draining both at the top and bottom undergoes 50 percentconsolidation in 16 years under an applied load. If an additional drainage layerwere present at the middle of the clay stratum, 50 percent consolidation wouldoccur in(A) 2 years (B) 4 years (C) 8 years (D) 16 years

Q.49 A test plate 30cm x 30cm resting on a sand deposit settles by 10mm under acertain loading intensity. A footing 150cm x 200cm resting on the same sanddeposit and loaded to the same load intensity settles by(A) 2.0mm (B) 27.8mm (C) 3.02mm (D) 50.0mm

Q.50 A volume of 3.0 x 106 m3 of groundwater was pumped out from an unconfinedaquifer, uniformly from an area of 5km2. The pumping lowered the water tablefrom initial level of 102m to 99m. The specific yield of the aquifer is(A) 0.20 (B) 0.30 (C) 0.40 (D) 0.50

Q.51 A weir on a permeable foundation with down-stream sheet pile is shown in thefigure below. the exit gradient as per Khosla’s method is

8


Q.52 Water emerges from an ogee spillway with velocity = 13.72 m/s and depth = 0.3mat its toe. The tail water depth required to form a hydraulic jump at the toe is

(A) 6.48m (B) 5.24m (C) 3.24m (D) 2.24m

Q.53 The flow of water (mass density = 1000 kg/m3 and kinematic viscosity = 10-6

m2/s) in a commercial pipe, having equivalent roughness ks as 0.12mm, yields anaverage shear stress at the pipe boundary = 600 N/m2 . The value of ks / ’ ( ’being the thickness of laminar sub-layer) for this pipe is

(A) 0.25 (B) 0.50 (C) 6.0 (D) 8.0

Q.54 A river reach of 2.0km long with maximum flood discharge of 10000m3 /s is to bephysically modeled in the laboratory where maximum available discharge is0.20m3/s. For a geometrically similar model based on equality of Froude number,the length of the river reach (m) in the model is

(A) 26.4 (B) 25.0 (C) 20.5 (D) 18.0

Q.55 An outlet irrigates an area of 20ha. The discharge (I/s) required at this outlet tomeet the evapotranspiration requirement of 20mm occurring uniformly in 20 daysneglecting other field losses is

(A) 2.52 (B) 2.31 (C) 2.01 (D) 1.52

Q.56 A wastewater sample contains 10-56 mmol /I of OH- ions at 25o C. The pH of thissample is

(A) 8.6 (B) 8.4 (C) 5.6 (D) 5.4

Q.57 Group I lists estimation methods of some of the water and wastewater qualityparameters. Group II lists the indicators used in the estimation methods. Matchthe estimation method (Group I) with the corresponding indicator (Group II).

P.

Q.

R.

S.

Azide modified Winklermethod for dissolved oxygenDichromate method forchemical oxygen demandEDTA titrimetric method forhardnessMohr or Argentometricmethod for chlorides

1. Eriochrome Black T

2. Ferrion

3. Potassium chromate

4. Starch

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

(B) P-4, Q-2, R-1, S-3(D) P-4, Q-2, R-3, S-1

9


Q.58 Determine the correctness or otherwise of the following Assertion [a] and Reason [r] The crown of the outgoing larger diameter sewer is always matched

with the crown of incoming smaller diameter sewer.

It eliminates backing up of sewage in the incoming smaller diametersewer.(A) Both [a] and [r] are true and [r] is the correct 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 true but [r] is false

Q.59 The 5-day BOD of a wastewater sample is obtained as 190mg/I (with k = 0.01h-1).The ultimate oxygen demand (mg/I) of the sample will be(A) 3800 (B) 475 (C) 271 (D) 190

Q.60 A water treatment plant is required to process 28800m3/d of raw water (density =1000kg/m3, kinematic viscosity = 10-6m2/s). The rapid mixing tank imparts avelocity gradient of 900s-1 to blend 35mg/I of alum with the flow for a detentiontime of 2 minutes. The power input (W) required for rapid mixing is

(A) 32.4 (B) 36 (C) 324 (D) 32400

Q.61 Match Group I (Terminology) with Group II (Definition / Brief Description) forwastewater treatment systems

P.

Q.

Primary treatment

Secondary treatment

1. Contaminant removal byphysical forces

2. Involving biological and / or

R.

S.

Unit operation

Unit process

chemical reaction3. Conversion of soluble organic

matter to business4. Removal of solid materials

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

from incoming wastewater

(B) P-4, Q-3, R-2, S-1(D) P-1, Q-2, R-3, S-4

Q.62 A roundabout is provided with an average entry width of 8.4m, width of weavingsection as 14m, and length of the weaving section between channelizing islands as35m. the crossing traffic and total traffic on the weaving section are 1000 and2000 PCU per hour respectively. The nearest rounded capacity of the roundabout(in PCU per hour) is

(A) 3300 (B) 3700 (C) 4500 (D) 5200

10


Q.63 Design parameters for a signalized intersection are shown in the figure below. thegreen time calculated for major and minor roads are 34 and 18s, respectively.

The critical land volume on the major road changes to 440 vehicles per hour perlane and the critical lane volume on the minor road remains unchanged. The greentime will

(A) increase for the major road and remain same for the minor road.(B) Increase for the major road and decrease for the minor road.(C) Decrease for both the roads.(D) Remain unchanged for both the roads.

Q.64 It is proposed to widen and strengthen an existing 2-lane NH section as a dividedhighway. The existing traffic in one direction is 2500 commercial vehicles (CV)per day. The construction will take 1 year. The design CBR of soil subgrade isfound to be 5 percent. Given: traffic growth rate for CV = 8 percent, vehicledamage factor = 3.5 (standard axles per CV), design life = 10 years and trafficdistribution factor = 0.75. The cumulative standard axles (msa) computed are

(A) 35 (B) 37 (C) 65 (D) 70

Q.65 A linear relationship is observed between speed and density on a certain sectionof a highway. The free flow speed is observed to be 80 km per hour and the jamdensity is estimated as 100 vehicles per km length. Based on the aboverelationship, the maximum flow expected on this section and the speed at themaximum flow will respectively be(A) 8000 vehicles per hour and 80km per hour(B) 8000 vehicles per hour and 25km per hour(C) 2000 vehicles per hour 80km per hour.(D) 2000 vehicles per hour and 40km per hour

11


Q.66 The plan of a survey plotted to a scale of 10m to 1cm is reduced in such a waythat a line originally 10cm long now measures 9cm. the area of the reduced plan ismeasured as 81cm2. the actual (m2) of the survey is(A) 10000 (B) 6561 (C) 1000 (D) 656

Q.67 The length and bearings of a closed traverse PQRSP are given below.

PQ

QR

RS

SP

200

1000

907

?

0o

45o

180o

?

The missing length and bearing, respectively of the line SP are(A) 207m and 2700

(C) 707m and 1800(B) 707m and 2700

(D) 907m and 2700

Q.68 The focal length of the object glass of a tacheometer is 200mm, the distancebetween the vertical axis of the tacheometer and the optical centre of the objectglass is 100mm and the spacing between the upper and lower line of thediaphragm axis is 4mm. with the line of collimation perfectly horizontal, the staffintercepts are 1m (top), 2m (middle), and 3m (bottom). The horizontal distance(m) between the staff and the instrument station is

(A) 100.3 (B) 103.0 (C) 150.0 (D) 153.0

Q.69 A road is provided with a horizontal circular curve having deflection angle 550

and centre line radius of 250m. A transition curve is to be provided at each end ofthe circular curve of such a length that the rate of gain of radial acceleration is0.3m/s3 at a curve required at each of the ends is

(A) 2.57m (B) 33.33m (C) 35.73m (D) 1666.67m

Q.70 A light house of 120m height is just visible above the horizon from a ship. Thecorrect distance (m) between the ship and the light house considering combinedcorrection for curvature and refraction, is

(A) 39.098 (B) 42.226 (C) 39098 (D) 42226

A rectangular channel 6.0m wide carries a discharge of 16.0m3/s under uniform conditionwith normal depth of 1.60m. Manning’s n is 0.015.

12


Q.71 The longitudinal slope of the channel is(A) 0.000585 (B) 0.000485 (C) 0.000385 (D) 0.000285

Q.72 A hump is to be provided on the channel bed. The maximum height of the humpwithout affecting the upstream flow condition is

(A) 0.50m (B) 3.8m (C) 4.1m (D) 4.5m

Q.73 The channel width is to be contracted. The minimum width to which the channelcan be contracted without affecting the upstream flow condition is(A) 3.0m (B) 3.8m (C) 4.1m (D) 4.5m

A reinforced concrete beam of rectangular cross section of breadth 230mm and effectivedepth 400mm is subjected to maximum factored shear force of 120kN. The grades ofconcrete, main steel and stirrup steel are M20, Fe415 and Feb250 respectively. For thearea of main steel provided, the design shear strength c is per IS: 456-2000 is 0.48N /mm2. The beam is designed for collapse limit state.

Q.74 The spacing (mm) of 2-legged 8mm stirrups to be provided is

(A) 40 (B) 115 (C) 250 (D) 400

Q.75 In addition, the beam is subjected to a torque whose factored value is 10.90kNm.the stirrups have to be provided to carry a shear (kN) equal to

(A) 50.42 (B) 130.56 (C) 151.67 (D) 200.23

Beam GHI is supported by these pontoons as shown in the figure below. the horizontalcross-sectional area of each pontoon is 8m2, the flexural rigidity of the beam is 10000kN-m2 and the unit weight of water is 10kN-m3.

13


Q.76 When the middle pontoon is removed, the deflection at H will be(A) 0.2m (B) 0.4m (C) 0.6m (D) 0.8m

Q.77 When the middle pontoon is brought back to its position as shown in the figureabove, the reaction at H will be(A) 8.6kN (B) 15.7kN (C) 19.2kN (D) 24.2kN

The ground conditions at a site are shown in the figure below

Q.78 The saturated unit weight of the sand (kN/m3) is(A) 15 (B) 18 (C) 21 (D) 24

Q.79 The total stress, pore water pressure and effective stress (kN/m2) at the point Pare, respectively(A) 75, 50 and 25(C) 105, 50 and 55

(B) 90, 50 and 40(D) 120, 50 and 70

A column is supported on a footing as shown in the figure below. the water table is at adepth of 10m below the base of the footing.

14


Q.80 The net ultimate bearing capacity (kN/m2) of the footing based on Terzaghi’sbearing capacity equation is(A) 216 (B) 432 (C) 630 (D) 846

Q.81 The safe load (kN) that the footing can carry with a factor of safety 3 is

(A) 282 (B) 648 (C) 945 (D) 1269

An automobile with projected area 2.6m2 is running on a road with speed of 120km perhour. The mass density and the kinematic viscosity of air are 1.2 kg/m3 and 1.5x10-5m2 /s,respectively. The drag coefficient is 0.30.

Q.82 The drag force on the automobile is(A) 620N (B) 600N (C) 580N (D) 520N

Q.83 The metric horse power required to overcome the drag force is(A) 33.23 (B) 31.23 (C) 23.23 (D) 20.23

A horizontal circular curve with a centre line radius of 200m is provided on a 2-lane, 2-way SH section. The width of the 2-lane road is 7.0m. Design speed for this section is 80km per hour. The brake reaction time is 2.4s, and the coefficients of friction inlongitudinal and lateral directions are 0.355 and 0.15, respectively.

Q.84 The safe stopping sight distance on the section is

(A) 221m (B) 195m (C) 125m (D) 65m

Q.85 The set-back distance from the centre line of the inner lane is

(A) 7.93m (B) 8.10m (C) 9.60m (D) 9.77m

15

1 1 3

The minimum and the maximum eigen values of the matrix 1 5 1 are -2 and

6, respectively. What is the other eigen value? 3 1 1

5 (B) 3 (C) 1

2

3 = 0 is

(D) -1

The degree of the differential equation 2 2

0 (B) 1 (C) 2

2

(D) 3

Q.3 The solution for the differential equationx=0 is

with condition that y = 1 at

1 3 2 3

(A) 2

( ) ln( ) 43

( ) ln( )2 3

( )

Q.4 An axially loaded bar is subjected to a normal stress of 173 MPa. The shear stressin the bar is

(A) 75MPa (B) 86.5MPa (C) 100MPa (D) 122.3MPa

Q.5 A steel column, pinned at both ends, has a buckling load of 200kN. If the columnis restrained against lateral movement at its mid-height, its buckling load will be

(A) 200kN (B) 283kN (C) 400kN (D) 800kN

Q.6 The stiffness coefficient kij indicates(A) force at i due to a unit deformation at j.(B) deformation at j due to a unit force at i.(C) deformation at i due to a unit force at j.(D) force at j due to a unit deformation at i.

Q.7 For an isotropic material, the relationship between the Young’s modulus (E),shear modulus (G) and Poisson’s ratio ( ) is given by

( ) ( ) ( ) ( )2(1 ) 2(1 ) (1 2 ) 2(1 )

1


Q.8 A clay soil sample is tested in triaxial apparatus in consolidated-drainedconditions at a cell pressure of 100 kN/m2. What will be the pore water pressure ata deviator stress of 40kN/m2?

(A) 0kN /m2 (B) 20kN/m2 (C) 40kN/m2 (D) 60kN/m2

Q.9 The number of blows observed in a Standard Penetration Test (SPT) for differentpenetration depths are given as follows.

0-150mm

150-300mm

300-450mm

The observed N value is(A) 8 (B) 14

6

8

10

(C) 18 (D) 24

Q.10 The vertical stress at some depth below the corner of a 2m x 3m rectangularfooting due to a certain load intensity is 100 kN / m2 below the centre of a4m x 6m rectangular footing at the same depth and same load intensity?(A) 25 (B) 100 (C) 200 (D) 400

Q.11 There is a free overfall at the end of a long open channel. For a given flow rate,the critical depth is less than the normal depth. What gradually varied flow profilewill occur in the channel for this flow rate?(A) M1 (B) M2 (C) M3 (D) S1

Q.12 The consumptive use of water for a crop during a particular stage of growth is2.0mm / day. The maximum depth of available water is the root zone is 60mm.Irrigation is required when the amount of available water is 50% of the maximumavailable water in the root zone. Frequency of irrigation should be(A) 10 days (B) 15days (C) 20days (D) 25days

Q.13 As per the Lacey’s method for design of alluvial channels, identity the truestatement from the following(A) Wetted perimeter increases with an increase in design discharge(B) Hydraulic radius increases with an increase in silt factor.(C) Wetted perimeter decreases with an increase in design discharge.(D) Wetted perimeter increases with an increase in silt factor.

Q.14 At two points 1 and 2 in a pipeline the velocities are V and 2V, respectively. Boththe points are at the same elevation. Both the points are at the same elevation. The

2


fluid density is . The flow can be assumed to be in compressible, inviscid, steadyand irrotational. The difference in pressures P1 and P2 at points 1 and 2 is

(A) 0.5 V2 (B) 1.5 V2 (C) 2 V2 (D) 3 V2

Q.15 The presence of hardness in excess of permissible limit causes(A) Cardio Vascular problems(C) Calcium deficiency

(B) Skin discolouration(D) Increased laundry expenses

Q.16 The dispersion of pollutants in atmosphere is maximum when(A) environmental lapse rate is greater than adiabatic lapse rate.(B) environmental lapse rate is less than adiabatic lapse rate.(C) environmental lapse rate is equal to adiabatic lapse rate.(D) maximum mixing depth is equal to zero.

Q.17 The alkalinity and the hardness of a water sample are 250mg/L and 350 mg/L asCaCo3, respectively. The water has(A) 350 mg/L carbonate hardness and zero non-carbonate hardness.(B) 250mg/L carbonate hardness and zero non-carbonate hardness.(C) 250mg/L carbonate hardness and 350 mg/L non-carbonate hardness.(D) 250mg/L carbonate hardness and 100 mg/L non-carbonate hardness.

Q.18 The consistency and flow resistance of bitumen can be determined from thefollowing.(A) Ductility test(C) Softening point Test

(B) Penetration test(D) Viscosity test

Q.19 If a two-lane national highway and a two-lane state highway intersect at rightright angles, the number of potential conflict points at the intersection, assumingthat both the roads are two-way is(A) 11 (B) 17 (C) 24 (D) 32

Q.20 In signal design as per Indian Roads Congress specifications, if the sum of theratios of normal flows to saturation flow of two directional traffic flow is 0.50 andthe total lost time per cycle is 10 seconds, the optimum cycle length in seconds is(A) 100 (B) 80 (C) 60 (D) 40

Q.21 For what values of and the following simultaneous equations have an infinitenumber of solutions?x + y + z = 5;x + 2y + z =

x + 3y + 3z = 9;

(A) 2,7 (B) 3,8 (C) 8,3 (D) 7,2

3

Q.22 A velocity vector is given as


r r 2 r 2 r5 2 3 .

The divergence of this velocity vector at (1,1,1) is(A) 9 (B) 10 (C) 14 (D) 15

Q.23 A body originally at 600C cools down to 400C in 15minutes when kept in air at atemperature of 250C. What will be the temperature of the body at the end of30minutes?(A) 35.20C (B) 31.50C (C) 28.70C (D) 150C

Q.24 The following equation needs to be numerically solved using the Newton-Raphson method.

x3 + 4x – 9 = 0The iterative equation for this purpose is (k indicates the iteration level)

2 3 9 3 2 4

( ) 12

34 ( ) 1

22

9

2 4 2 3

( ) 34

( )1

sin1

29

2

Q.25 Evaluate0

( )

dt

( )2

( )4

( )3

Q.26 Potential function is givenas

2 2

. What will be the stream function

( ) with the condition = 0 at x = y = 0?

(A) 2xy (B) x2 + y2

(C) x2 – y2

1 2

(D) 2x2y2

Q.27 The inverse of the 2 x 2 matrix is

1 7 2

5 7

1 7 2( ) ( )

3 5 1 3 5 1

( ) 1 7 2 ( ) 1 7 2

3 5 1 3 5 1

Q.28 Given that one root of the equation x3-10x2+31x-30=0 is 5, the other two roots are(A) 2 and 3 (B) 2 and 4 (C) 3 and 4 (D) -2 and -3

4


Q.29 If the standard deviation of the spot speed of vehicles in a highway is 8.8 kmphand the mean speed of the vehicles is 33kmph, the coefficient of variation inspeed is(A) 0.1517 (B) 0.1867 (C) 0.2666 (D) 0.3646

Q.30 A metal bar of length 100mm is inserted between two rigid supports and itstemperature is increased by 100C. If the coefficient of thermal expansion is 12 x10-6 per 0C and the Young’s modulus is 2 x 105 MPa, the stress in the bar is(A) zero (B) 12MPa (C) 24MPa (D) 2400MPa

Q.31 A rigid bar is suspended by three rods made of the same material as shown in thefigure. The area and length of the central rod are 3A and L, respectively while thatof the two outer rods are 2A and 2L respectively. If a downward force of 50kN isapplied to the rigid bar, the forces in the central and each of the outer rods will be(A) 16.67 kN each(C) 30kN and 10kN

(B) 30kN and 15kN(D) 21.4kN and 14.3kN

Q.32 The maximum and minimum shear stresses in a hollow circular shaft of outerdiameter 20mm and thickness 2mm, subjected to a torque of 92.7 N.m will be(A) 59 MPa and 47.2 MPa(C) 118 MPa and 160 MPa

(B) 10MPa and 80MPa(D) 200 MPa and 160 MPa

Q.33 The shear stress at the neutral axis in a beam of triangular section with a base of40mm and height of 20mm, subjected to a shear force of 3kN is(A) 3MPa (B) 6MPa (C) 10MPa (D) 20MPa

Q.34 U1 and U2 are the strain energies stored in a prismatic bar due to axial tensileforces P1 and P2 respectively. The strain energy stored in the same bar due tocombined action of P1 and P2 will be(A) U = U1 + U2

(C) U <U1 + U2

(B) U = U1 U2

(D) U >1 + U2

Q.35 The right triangular truss is made of members having equal cross sectional area of1550 mm2 and Young’s modulus of 2 x 105 MPa. The horizontal deflection of thejoint Q is

(A) 2.47mm (B) 10.25mm (C) 14.1mm (D) 15.68mm

5


Q.36 The influence line diagram (ILD) shown is for the member

(A) PS (B) RS (C) PQ (D) QS

Q.37 Consider the following statements:1.

2.

3.

The compressive strength of concrete decreases with increase in water-cement ratio of the concrete mix.Water is added to the concrete mix for hydration of cement andworkability.Creep and shrinkage of concrete are independent of the water-cement ratioin the concrete mix.

The true statements are(A) 1 and 2 (B) 1, 2 and 3 (C) 2 and 3 (D) only 2

Q.38 The percentage loss of prestress due to anchorage slip of 3mm in a concrete beamof length 30m which is post-tensioned by a tendon with an initial stress of 1200 N/ mm2 and modulus of elasticity equal to 2.1 x 105 N/mm2 is(A) 0.0175 (B) 0.175 (C) 1.75 (D) 17.5

Q.39 A concrete beam of rectangular cross-section of size 120mm (width) and 200mm(depth) is prestressed by a straight tendon to an effective force of 150kN at aneccentricity of 20mm (below the centroidal axis in the depth direction). Thestresses at the top and bottom fibres of the section are

(A) 2.5 N/mm2 (compression), 10N/mm2 (compression)(B) 10N / mm2 (tension), 3.75 N / mm2

(C) 3.75 N/mm2 (tension), 3.75 N/mm2 (compression)(D) 2.75 N/mm2 (compression), 3.75 N/mm2 (compression)

Q.40 Consider the following statements:I. Modulus of elasticity concrete increases with increase in compressive

strength of concrete.II. Brittleness of concrete increases with decrease in compressive strength of

concrete.

6


III. Shear strength of concrete increases with increase in compressive strengthof concrete.

The TRUE statements are(A) II and III (B) I, II and III (C) I and II (D) I and III

Q.41 A steel flat of rectangular section of size 70 x 6 mm is connected to a gusset plateby three bolts each having a shear capacity of 15kN in holes having diameter11.5mm. If the allowable tensile stress in the flat is 150MPa, the maximumtension that can be applied to the flat is

(A) 42.3kN (B) 52.65kN (C) 59.5kN (D) 63.0kN

Q.42 A bracket connection is made with four bolts of 10mm diameter and supports aload of 10kN a an eccentricity of 100mm. the maximum force to be resisted byany bolt will be

(A) 5kN (B) 6.5kN (C) 6.8kN (D) 7.16kN

Q.43 The plastic collapse load Wp for the propped cantilever supporting two point loadsas shown in the figure in terms of plastic moment capacity, Mp is given by

(A) 3Mp/L (B) 4Mp/L (C) 5 Mp/L (D) 6Mp/L

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Q.44 Sieve analysis on a dry soil sample of mass 1000g showed that 980g and 270g ofsoil pass through 4.75mm and 0.075mm sieve, respectively. The liquid limit andplastic limits of the soil fraction passing through 425 sieves are 40% and 18%respectively. The soil may be classified as

(A) SC (B) MI (C) CI (D) SM

Q.45 The water content of a saturated soil and the specific gravity of soil solids werefound to be 30% and 2.70, respectively. Assuming the unit weight of water to be10kN / m3, the saturated unit weight (kN/m3), and the void ratio of the soil are

(A) 19.4, 0.81 (B) 18.5, 0.30 (C) 19.4. 0.45 (D) 18.5, 0.45

Q.46 The factor of safety of an infinite soil slope shown in the figure having the0 3 3 is

properties c=0, 0, 35 , 16 / 20 /approximately equal to

(A) 0.70 (B) 0.80 (C) 1.00 (D) 1.20

Q.47 Match the following groups

P Constant head permeability test

Q Consolidation test

R Pycnometer test

S Negative skin friction

1. Pile foundations

2. Specific gravity

3. Clay soil

4. Sand

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

(B) P-4, Q-2, R-3, S-1(D) P-4, Q-1, R-2, S-3

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Q.48 The bearing capacity of a rectangular footing of plan dimensions 1.5m x 3mresting on the surface of a sand deposit was estimated as 600 kN/m2 when thewater table is far below the base of the footing. The bearing capacities in kN/m2

when the water level rises to depths of 3m, 1.5m and 0.5m below the base of thefooting are

(A) 600, 600, 400(C) 600, 500, 250

(B) 600, 450, 350(D) 600, 400, 250

Q.49 What is the ultimate capacity in kN of the pile group shown in the figureassuming the group to fail as a single block?

(A) 921.6 (B) 1177.6 (C) 2438.6 (D) 3481.6

Q.50 A horizontal water jet with a velocity of 10m/s and cross sectional area of 10mm2

strikes a flat plate held normal to the flow direction. The density of water is 1000kg/m3. The total force on the plate due to the jet is

(A) 100N (B) 10N (C) 1N (D) 0.1N

Q.51 A 1:50 scale model of a spillway is to be tested in the laboratory. The discharge inthe prototype is 1000M3 /s. The discharge to be maintained in the model test is

(A) 0.057m3/s (B) 0.08m2/s (C) 0.57m3/s (D) 5.7m3/s

Q.52 A triangular open channel has a vertex angle of 900 and carries flow at a criticaldepth of 0.30m. the discharge in the channel is(A) 0.08m3/s (B) 0.11 m3/s (C) 0.15 m3/s (D) 0.2 m3/s

Q.53 Flow rate of a fluid (density = 1000kg/m3) in a small diameter tube is 800 m3/s.The length and the diameter of the tube are 2m and 0.5mm, respectively. Thepressure drop in 2m length is equal to 2.0MPa. The viscosity of the fluid is

(A) 0.025N.s/m2 (B) 0.012N.s/m2 (C) 0.0092 N.s/m2(D) 0.00102 N.s/m2

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Q.54 The flow rate in a wide rectangular open channel is 2.0m3/s per meter width. Thechannel bed slope is 0.002. The Manning’s roughness coefficient is 0.012. Theslope of the channel is classified as

(A) Critical (B) Horizontal (C) Mild (D) Steep

Q.55 The culturable command area for a distributary channel is 20,000 hectares. Wheatgrown in the entire area and the intensity of irrigation is 50%. The kor period forwheat is 30 days and the kor water depth is 120mm. The outlet discharge for thedistributary should be

(A) 2.85m3/s (B) 3.21m3/s (C) 4.63m3/s (D) 5.23m3/s

Q.56 An isolated 4-hour storm occurred over a catchment as follows

TimeRainfall (mm)

1st hour9

2nd hour28

3rd hour12

4th hour7

The index for the catchment is 10mm/h. The estimated runoff depth from thecatchment due to the above storm is

(A) 10mm (B) 16mm (C) 20mm (D) 23mm

Q.57 Two electrostatic precipitators (ESPs) are in series. The fractional efficiencies ofthe upstream and downstream ESPs for size dp are 80% and 65%. Respectively.What is the overall efficiency of the system for the same dp?

(A) 100% (B) 93% (C) 80% (D) 65%

Q.58 50g of CO2 and 25g of CH4 are produced from the decomposition of municipalsolid waste (MSW) with a formula weight of 120g. What is the average per capitagreen house gas production in a city of 1 million people with a MSW productionrate of 500 ton / day?(A) 104 g/day (B) 120 g/day (C) 208 g/day (D) 313 g /day

Q.59 The extra widening required for a two-lane national highway at a horizontal curveof 300 m radius, considering a wheel base of 8m and a design speed of 100kmphis(A) 0.42m (B) 0.62m (C) 0.82m (D) 0.92m

Q.60 While designing a hill road with a ruling gradient of 6%, if a sharp horizontalcurve of 50m radius is encountered, the compensated gradient at the curve as perthe Indian Roads Congress specifications should be(A) 4.4% (B) 4.75% (C) 5.0% (D) 5.25%

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Q.61 The design speed on a road is 60kmph. Assuming the driver reaction time of 2.5seconds and coefficient of friction of pavement surface as 0.35, the requiredstopped distance for two-way traffic on a single lane road is(A) 82.1m (B) 102.4 (C) 164.2m (D) 186.4m

Q.62 The width of the expansion joint is 20mm in a cement concrete pavement. Thelaying temperature is 200C and the maximum slab temperature in summer is 600C.The coefficient of thermal expansion of concrete is 10 x 10-6 mm/mm / 0C and thejoint filler compresses upto 50% of the thickness. The spacing between expansionjoints should be(A) 20m (B) 25m (C) 30m (D) 40m

Q.63 The following data pertains to the number of commercial vehicles per day for thedesign of a flexible pavement for a national highway as per IRC: 37-1984Type of commercial Number of vehicles per dayVehicle Damage Factorvehicle considering the number of lanesTwo axle trucks 2000 5Tandem axle trucks 200 6

Assuming a traffic growth factor of 7.5% per annum for both the types ofvehicles, the cumulative number of standard axle load repetitions (in million) fora design life of ten years is(A) 44.6 (B) 57.8 (C) 62.4 (D) 78.7

Q.64 Match the following tests on aggregate and its properties

P.

Q.

R.

S.

Crushing Test

Los Angles abrasion test

Soundness test

Angularity test

1.

2.

3.

4.

Hardness

Weathering

Shape

Strength

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

(B) P-4, Q-2, R-3, S-1(D) P-4, Q-1, R-2, S-2

Q.65 The plan of a map was photo copied to a reduced size such that a line originally100mm, measures 90mm. The original scale of the plan was 1:1000. The revisedscale is(A) 1:900 (B) 1:11111 (C) 1:1121 (D) 1:1221

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Q.66 The following table gives data of consecutive coordinates in respect of a closedtheodolite traverse PQRSP.

P

Q

R

S

400.75

100.25

199.0

300.0

300.5

199.25

399.75

200.5

The magnitude and direction of error of closure in whole circle bearing are

(A) 2.0m and 450

(C) 2.82m and 3150(B) 2.0m and 3150

(D) 3.42m and 450

Q.67 The following measurements were made during testing a leveling instrument.

P

Q

2.800m

2.700m

1.700m

1.800m

P1 is close to P and Q1 is close to Q. If the reduced level of station P is 100.000m,the reduced level of station Q is(A) 99.000m (B) 100.000m (C) 101.000m (D) 102.000m

Q.68 Two straight lines intersect at an angle of 600. The radius of a curve joining thetwo straight lines is 600m. The length of long chord and mid-ordinates in metresof the curve are(A) 80.4, 600.00 (B) 600.0, 80.4 (C) 600.0, 39.89 (D) 40, 89,300

Q.69 The magnetic bearing of a line AB is S 450 E and the declination is 50 West. Thetrue bearing of the line AB is(A) S 450 E (B) S 400 E (C) S 500 E (D) S 500 W

Water is flowing through the permeability apparatus as shown in the figure. Thecoefficient of permeability of the soil is km/s and the porosity of the soil sample is0.50.

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Q.70 The total head, elevation head and pressure head in metres of water at the point Rshown in the figure are

(A) 0.8, 0.4, 0.4(C) 0.4, 0, 0.4

(B) 1.2, 0.4, 0.8(D) 1.6, 0.4, 1.2

Q.71 What are the discharge velocity and seepage velocity through the soil sample?(A) k, 2k (B) 2/3k, 4/3k (C) 2k,k (D) 4/3k, 2/3k

Ordinates of a 1-hour unit hydrograph at 1 hour intervals, starting from time t = 0,are 0, 2, 6,4,2,1 and 0 m3/s.

Q.72 Catchment area represented by this unit hydrograph is

(A) 1.0 km2 (B) 2.0 km2 (C) 3.2 km2 (D) 5.4 km2

Q.73 Ordinate of a 3-hour unit hydrograph for the catchment at t=3 hours is

(A) 2.0m3/s (B) 3.0m3/s (C) 4.0m3/s (D) 5.0m3/s

A completely mixed activated sludge process is used to treat a wastewater flow of1 million litres per day (1 MLD) having a BOD5 of 200 mg/L. The biomassconcentration in the aeration tank is 2000 mg/L and the concentration of the netbiomass leaving the system of 50mg/L. the aeration tank has a volume of 200 m3.

Q.74 What is the hydraulic retention time of the wastewater in aeration tank?

(A) 0.2h (B) 4.8h (C) 10h (D) 24h

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Q.75 What is the average time for which the biomass stays in the system?

(A) 5h (B) 8h (C) 2days (D) 8 days

A two span continuous beam having equal spans each of length L is subjected to auniformly distributed load per unit length. The beam has constant flexuralrigidity.

Q.76 The reaction at the middle support is2

(A) L (B) 5 2 (C) 5 4 (D) 16

A singly reinforced rectangular concrete beam has a width of 150mm and an effectivedepth of 330mm. The characteristic compressive strength of concrete is 20 MPa. Adoptthe stress block for concrete as given in IS 456-2000 and take limiting value of depth ofneutral axis as 0.48 times the effective depth of the beam.

Q.78 The limiting value of the moment of resistance of the beam is kN.m is

(A) 0.14 (B) 0.45 (C) 45.08 (D) 156.82

Q.79 The limiting area of tension steel in mm2 is(A) 473.9 (B) 412.3 (C) 373.9 (D) 312.3

The ground conditions at a site are as shown in the figure. The water table at thesite which was initially at a depth of 5m below the ground level got permanentlylowered to a depth of 15m below the ground level due to pumping of water over afew years. Assume the following data

i. unit weight of water = 10kN/m3

ii. unit weight of sand above water table = 18kN/m3

iii. unit weight of sand and clay below the water table = 20kN/m3

iv. coefficient of volume compressibility = 0.25m2/MN

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Q.80 What is the change in the effective stress in kN/m2 at mid-depth of the clay layerdue to the lowering of the water table?(A) 0 (B) 20 (C) 80 (D) 100

Q.81 What is the compression of the clay layer in mm due to the lowering of the watertable?(A) 125 (B) 100 (C) 25 (D) 0

A rectangular open channel needs to be designed to carry a flow of 2.0m3/s underuniform flow conditions. The Manning’s roughness coefficient is 0.018. Thechannel should be such that the flow depth is equal to half the width, and theFroude number is equal to 0.5.

Q.82 The bed slope of the channel to be provided is(A) 0.0012 (B) 0.0021 (C) 0.0025 (D) 0.0052

Q.83 Keeping the width, flow depth and roughness the same, if the bed slope of theabove channel is doubled, the average, boundary shear stress under uniform flowconditions is(A) 5.6 N/m2 (B) 10.8 N/m2 (C) 12.3 N/m2 (D) 17.2 N/m2

A plain sedimentation tank with a length of 20m, width of 10m, and a depth of 3mis used in a water treatment plant to treat 4 million litres of water per day (4MLD). The average temperature of water is 200C. The dynamic viscosity of wateris 1.002 x 10-3 N.s/m2 at 200 C. Density of water is 998.2 kg/M3. Average specificgravity of particles is 2.65.

Q.84 What is the surface overflow rate in the sedimentation tank?(A) 20m3 / m2 / day(C) 67m3 / m2 / day

(B) 40m3 / m2 / day(D) 133m3 / m2 / day

Q.85 What is the minimum diameter of the particle which can be removed with 100%efficiency in the above sedimentation tank?

(A) 11.8 x 10-3 mm(C) 50 x 10-3 mm

(B) 16.0 x 10-3 mm(D) 160 x 10-3 mm

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civil engineering gate previous papers 2012-2000

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