Here is the Civil Engineering GATE Exam sample written Multiple Choice Question paper.
GATE – 1998
CE : Civil Engineering
Section A
(100 marks)
1. For each subquestion given below four answers are provided out of which only one is correct. Indicate in the answer book the correct or most appropriate answer by writing the letter A,B,C or D against the subquestion number. (31×1=31)
1.1 If A is a real square matrix, then AA^{T} is
(a) unsymmetric (b) always symmetric
(c) skew symmetric (d) sometimes symmetric
1.2 In matrix algebra AS = AT (A,S,T, are matrices of appropriate order) implies S=T only if
(a) A is symmetric (b) A is singular
(c) A is non singular (d) A is skew symmetric
1.3 A discontinuous real function can be expressed as
(a) Taylor’s series and Fourier’s series
(b) Taylor’s series and not by Fourier’s series
(c) neither Taylor’s series nor Fourier’s series
(d) not by Taylor’s series, but by Fourier’s series
1.4 The Laplace Transform of a unit step function u_{a}(T), defined as
0for1<a
Ua(t)= is
1 fort >a
(a) e^{as}/s (b)se^{as}
(c) su(0) (d) se^{as}1
1.5 The continuous function ƒ(x,y) is said to have saddle point at (a,b) if
(a) ƒ_{x} (a,b)= ƒ_{y}(a,b) = 0; ƒ_{sy}^{2} ƒ_{xx} ƒ_{yy}<0 at (a,b)
(b) ƒ_{x} (a,b)= 0; ƒ_{y}(a,b) = 0; ƒ_{xy}^{2} ƒ_{xx} . ƒ_{yy}>0 at (a,b)
(c) ƒ_{x} (a,b)= 0; ƒ_{y}(a,b) = 0; ƒ_{xx} and ƒ_{yy}<0 at (a,b)
(d) ƒ_{x} (a,b)= 0; ƒ_{y}(a,b) = 0; ƒ_{xx}^{2} – ƒ_{xx} . ƒ_{yy = }0 at (a,b)
1.6 The Taylor’s series expansion of sin x is
x^{2} x^{4} x^{2} x^{4}
(a) 1 + (b) 1+
2! 4! 2! 4!
x^{3} x^{5} x^{3} x^{5}
(a) x+ + (b) x
3! 5! 3! 5!
1.7 A three hinged arch shown in Figure is quarter of a circle. If the vertical and horizontal components of reaction at A are equal, the value of θ is
(a) 60^{0}
(b) 45^{0}
(c) 30^{0}
(d) None in (0^{0},90^{0})
1.8 A propped cantilever beam is shown in Figure. The plastic moment capacity of the beam is M_{0}. The collapse load P is
(a) 4M_{0}/L (b) 6M_{0}/L
(c) 8M_{0}/L (d) 12M_{0}/L
1.9 The maximum permissible deflection for gantry gride, spanning over 6m, on which an EOT (electric overhead travelling) crane of capacity 200 k.N is operating, is
(a) 8mm (b) 10mm
(c) 12mm (d0 18mm
1.10 An isolated T beam is used as a walkway. The beam is simply supported with an effective span of 6m. The effective width of flange, for the crosssection shown in Figure, is
(a) 900 mm
(b) 1000 mm
(c) 1259 mm
(d) 2200 mm
1.11 The plane of stairs supported at each end by landings spanning parallel with risers is shown in Figure. The effective span of staircase slab is
(a) 3000 mm (b) 4600 mm
(c) 4750 mm (d) 6400 I
1.12 Some of the structural strength of a clayey material that is lost by remoulding is slowly recovered with time. This property of soils to undergo an isothermal gelto soltoget transformation upon agitation and subsequent rest is termed
(a) Isotropy (b) Anisotropy
(c) Thixotropy (d) Allotropy
1.13. If soil is dried beyond its shrinkage limit, it will show
(a) Large volume change
(b) Moderate volume change
(c) Low volume change
(d) No volume change
1.14. The stressstrain behaviour of soils as shown in the Figure correspondence to :
(a) Curve 1 : Loose sand and normaly consolidated clay
Curve 2 : Loose sand and over consolidated clay
(b) Curve 1 : Dense sand and normally consolidated clay
Curve 2 : Loose sand and over consolidated clay
(c) Curve 1 : Dense sand and over consolidated clay
Curve 2 : Loose sand and normally consolidated clay
(d) Curve 1 : Loose sand and over consolidated clay
Curve 2 : Dense sand normally consolidated clay
1.15 In cohesive soils he depth of tension crack (Z_{cr}) is likely to be
1.16 The settlement of prototype in granular material may be estimated using plate load test data from the following expression :
1.17 In which one of the following arrangement would the vertical force on the cylinder due to water be the maximum ?
1.18. At the same mean velocity, the ratio of head loss per unit length for a sewer pipe flowing full to that for the same pipe flowing half full would be
(a) 2.0 (b) 1.63
(c) 1.00 (d) 0.61
1.19 Three reservoirs A, B and C are interconnected by pipes as shown in the Figure. Water surface elevations in the reservoirs and the Pirzometric head at the junction J are indicated in the Figure.
Discharge Q_{1}, Q_{2} and Q_{3} are related as
(a) Q_{1}+Q_{2} = Q_{3} (b) Q_{1}=Q_{2}+Q_{3}
(c) Q_{2}=Q_{1}+Q_{3} (d) Q1+Q_{2}+Q_{3} = 0
1.20. The comparison between pumps operating in series and in parallel is
(a) Pumps operating is series boost the discharge, whereas pumps operating in parallel boost the head.
(b) Pumps operating in parallel boost the discharge, whereas pumps operating in series boost the head.
(c) In both cases there would be a boost in discharge only.
(d) In both case there would be a boost in head only.
1.21 The Bowen ratio is defined as
(a) Ratio of heat and vapour diffusivities
(b) Proportionality constant between vapour heat flux and sensible ehat flux.
(c) Ratio of actual evaportranspiration and potential evaportranspiration.
(d) Proportionality constant between heat energy used up in evaporation and the bulk radiation from a water body.
1.23. Excessive fluoride in drinking water causes
(a) Alzheimer’s disease
(b) Mottling of teeth and embrittlement of bones
(c) Methemoglobinemia
(d) Skin cancer
1.24 Coagulationflocculation with alum is performed
(a) immediately before chlorination
(b) immediately after chlorination
(c) after rapid sand filtration
(d) before rapid sand filtration
1.25. Sewage treatment in an oxidation pond is accomplished primarily by
(a) algabacterial symbols
(b) algal photosynthesis only
(c) bacterial oxidation only
(d) chemical oxidation only
1.26 An inverted siphon is a
(a) device for distributing septic tank effluent to a soil absorption system
(b) device for preventing overflow from elevated water storage tank
(c) device for preventing crown corrosion of sewer
(d) section of sewer which is dropped below the hydraulic grade line in order to avoid an obstacle.
1.27 Water distribution systems are sized to meet the
(a) maximum hourly demand
(b) Average hourly demand
(c) maximum daily demand and fire demand
(d) average daily demand and fire demand.
1.28 At highway stretches where the required overtaking sight distance cannot be provided, it is necessary to incorporate in such sections the following
(a) at least twice the stopping sight distance
(b) half to the required overtaking sight distance
(c) one third of the required overtaking sight distance
(d) three times the stopping sight distance
1.29 The modulus of subgrade reaction is obtained from the plate bearing test in the form of loaddeformation curve. The pressure corresponding to the following settlement value should be used or computing modulus of subgrade reaction
(a) 0.375 cm (b) 0.175 cm
(c) 0.125 cm (d) 0.250 cm
1.30 In the plate bearing test, if the load applied is in the form of an inflated type of wheel, then this mechanism corresponds to
(a) rigid plate (b) flexible plate
(c) semirigid plate (d) semielastic plat e
1.31. Base course is used in rigid pavements for
(a) prevention of subgrade settlement
(b) prevention of slab cracking
(c) preventing of pumping
(d) preventing of thermal expansion
2. For each subquestion given below four answers are provided out of which one is correct. Indicate in the answer book the correct or most appropriate answer by writing the letter A,B, Cor Dagainst the subquestion number.
1 1 (22×2=44)
2.1 The infinite series 1+ + +…………
2 3
(a) converges (b) diverges
(c) oscillates (d) unstable
2.2 The real symmetric matrix C corresponding to the Quadratic form
Q=4x_{1}x_{2} – 5x_{22′} is
(a) 1 2 (b) 2 0
2 5 0 5
(c) 1 1 (d) 0 2
1 2 1 5
2.3 A cantilever beam is shown in the Figure. The moment to be applied at free end for zero vertical deflection at that point is
(a) 9 kN.m clockwise
(b) 9 kN.m anticlockwise
(c) 12kN.m clockwise
(d) 12kN.m anticlockwise
2.4. The strain energy stored in member AB of the pinjoined truss is shown in Fig. 2.4, when E and A are same for all members, is
(a) 2P^{2}L
AE
(b) P2L
AE
(c) P2L
2AE
(d) Zero
2.5 The stiffness matrix of a beam element is given as (2EI/L) 2 1. Then the flexibility matrix is 1 2
(a) L 2 1 (b) L 1 2
2EI 1 2 6EI 2 1
(a) L 2 1 (b) L 2 1
3EI 1 2 5EI 1 2
2.6 The plastic modulus of a section is 4.8×10^{4}m^{3}. The shape factor is 1.2. The plastic moment capacity of the section is 120 kN.m. The yield stress of the material is
(a) 100MPa (b) 240MPa
(c) 250MPa (d)300MPa
2.7. A reinforced concrete wall carrying vertical loads is generally designed as per recommendations given for columns. The ratio of minimum reinforcements in the vertical and horizontal directions is
(a) 2 :1 (b) 5:3
(c) 1:1 (d) 3:5
2.8. The proposed dam shown in the figure is 90 m long and the coefficient of permeability of the soil is 0.0013mm/second. The quantity of water (m^{3}) that will be lost per day be seepage is (rounded to the nearest number):
(a) 55 (b) 57
(c) 59 (d) 61
2.9 The time for a clay layer to achieve 90% consolidation is 15 years. The time required to achieve 90% consolidation, if the layer were twice as thick, 3 times more permeable and 4 times more compressible would be :
(a) 70 years (b) 75 years
(c) 80 years (d) 85 years
2.10. The total active thrust on a vertical wall 3m high retaining a horizontal sand backfill (unit weight γ_{t}=20 kN/m^{3}, angle of shearing resistance φ’=30^{0}) when the water table is at the bottom of the wall, will be :
(a) 30 kN/m (b) 35 kN/m
(c) 40 kN/m (d) 45 kN/m
2.11 A 40^{0} slope is excavated to a depth of 10(d)depth of 10 m is a deep layer of saturated clay of unit weight 20kN/m^{3}; the relevant shear strength parameters are c_{u}=72 kN/m^{2} and φ_{u}=0. The rock ledge is at a great depth. The Taylor’s stability coefficient for φ_{u}=0 and 400 slope angle is 0.18. The factor of safety of the load is :
(a) 2.0 (b) 2.1
(c) 2.2 (d) 2.3
2.12 A point load of 700 kN is applied on the surface of thick layer of saturated clay. Using Boussinesq’s elastic analysis, the estimated vertical stress (σ_{v}) at a depth of 2 m and a radial distance of 1.0 m from the point of application of the load is :
(a) 47.5 kPa (b) 47.6kPa
(c) 47.7 kPa (d) 47.8kPa
2.13 A nozzle discharging water under head H has an outlet area “a” and discharge coefficient c_{d}=1.0. A vertical plate is acted upon by the fluid force F_{j} when held across the free jet and by the fluid force F_{n} when held against the nozzle to stop the flow. The ratio
F_{j} is
F_{n}
(a) 1/2 (b) 1
(c) 2 (d) 2
2.14. A body moving through still water at 6m/sec produces a water velocity of 4m/sec at a point 1m ahead. The difference in pressure between the nose and the point 1m ahead would be
(a) 2,000N/m^{2} (b) 10,000N/m^{2}
(c) 19,620N/m^{2} (d) 98,100N/m^{2}
2.15 The return period for the annual maximum flood of a given magnitude is 8 years. The probability that this food magnitude will be exceeded once during the next 5 years is
(a) 0.625 (b) 0.966
(c) 0.487 (d) 0.529
2.16 Two completely penetrating wells are located L (in meters) apart, in a homogeneous confined aquifer. The drawdown measured at the mid point between the two wells (at a distance of 0.5L from both the wells) is 2.0 m when only he first well is being pumped at the steady rate of Q_{1}m^{3}/sec. When both the wells are being pumped at identical steady rate of Q2m^{3}/sec, the drawdown measured at the same location is 8.0m. It may be assumed that the drawdown at the wells always remains at 10.0 m when being pumped and the radius of influence is larger than Q^{1} is equal to
0.5L
Q^{2}
2.17. In connection with the design of a barrage, identify the correct matching of the criteria of design with the items of design

Item of design 

Criteria of design 
(i) 
Width of waterway 
(A) 
Scour depth and exit gradient 
(ii) 
Level and length of downstream floor 
(B) 
Lacey’s formula for wetted perimeter and discharge capacity of the barrage as computed by weir equations 
(iii) 
Depth of sheet piles and total of barrage floor 
(C) 
Uplift pressure variation 
(iv) 
Barrage floor thickness 
(D) 
Hydraulic jump considerations 
Codes :
(i) (ii) (iii) (iv)
(a) A B C D
(b) D C B A
(c) B A D C
(d) B D A C
2.18. In a BOD test using 5% dilution of the sample (15 ML of sample and 285 mL of dilution water), dissolved oxygen values for the sample and dilution water blank bottles after five days incubation at 20^{0}C were 3.80 and 8.80 mg/L, respectively. Dissolved oxygen originally present in the undiluted sample was 0.80 mg/L. The 5day 20^{0}C BOD of the sample is
(a) 116mg/L (b) 108 mg/L
(c) 100mg/L (d) 92 mg/L
2.19. For a flow of 5.7 MLD (million litres per day) and a detention time of 2 hours, the surface area of a rectangular sedimentation tank to remove all particles have setting velocity of 0.33 mm/s is
(a) 20m^{2} (b) 100m^{2}
(c) 200m^{2} (d) 400m^{2}
2.10. For a highway with design speed of 100 kmph, the safe overtaking sight distance is (assume acceleration as 0.53m/sec^{2}).
(a) 300m (b) 750m
(c) 320m (d) 470m
2.21 What is the equivalent wheel load of a dual wheel assembly carrying 20,440 N each for pavement thickness of 20 cm? Centre to centre spacing of tyres is 27cm and the distance between the walls of yres is 11cm.
(a) 27600 N (b) 32300N
(c) 40880N (d) 30190N
2.22 Plate bearing test with 20 cm diameter plate on soil subgrade yielded a pressure of 1.25×10^{5}N/m^{2} at 0.5 cm deflection. What is the elastic modulus of subgrade ?
(a) 56.18×10^{5}N/m^{2} (b) 22.10×10^{5}N/m^{2}
(c) 44.25×10^{5}N/m^{2} (d) 50.19×10^{5}N/m^{2}
3. Solve the following set of simultaneous equations by Gauss elimination method. (5)
x2y+z=3 …..(1)
x+3z=11 ……(2)
2y+z = 1 ……(3)
4. The crosssection of a pretensioned prestressed concrete beam is shown in Figure. The reinforcement is placed concentrically. If the stress in steel at transfer is 1000 MPa, compute the stress in steel immediately after transfer. The modular ratio is 6. (5)
5. An ISMS 400, with a flange width of 140 mm is subjected to an axial compressive load of 750 kN. Design the slab base resting on concrete of grade M15. The slab base available are 600x350x20 mm, 650x325x28mm, and 700x2300x32 mm. Select one of these. (5)
6. The total unit weight of the glacial outwash soil is 6kN/m^{3}. The specific gravity of the solid particles of the soil is 2.67. The water content of the soil is 17% Calculate. (5)
(a) dry unit weight (b) porosity
(c) void ratio (d) degree of saturation
Assume that unit weight of water (γ_{w}) is 10kN/m^{3}
7. An overflow spillway is 40 m high. Water flows down the spillway with a head of 2.5 m over the spillway crest. The spillway discharge coefficient
cd = 0.738. Show that the water depth at the toe of the spillway would be 0.3m. Determine the sequent depth required for the formation of the hydraulic jump and the loss of head in the jump. (5)
SECTIONB
(50 Marks)
Answer and TEN question from this section. All questions carry equal marks.
8. Solve d^{4}y – y = 15 cos 2x
dx^{4} (5)
9. Obtain the eigen values and eigen vectors of the matrix 8 4
2 2 (5)
10. Using the Force Method, computer the slope at the support B of the propped cantilever beam shown in Fig. 10. The value of EI is constant. (5)
11. The steel portal frame shown in Figure is subjected to an imposed service load of 15 kN. Compute the required plastic moment capacity of the members. All the members are of the same crosssection. Draw the collapse mode. (5)
12. Compute the bending moments at the top of the columns in the upper storey of the multistorey frame shown in Figure, by the cantilever the portal methods of analysis. Indicate tension face of columns, the area of crosssection of all columns is same.
13. The crosssection of a simply supported plate girder is shown in Figure. The loading on the girder is symmetrical. The bearing stiffeners at supports are the sole means of providing restraint against torsion. Design the bearing stiffeners at supports, with minimum moment of inertia about the centre line of web plate only as the sole design criterion. The flat section available are : 250×25, 250×32, 200×28, and 200×32 mm. Dray a sketch (5)
14. The diameter of a ring beam in water tank is 7.8 m. It is subjected to an outward raidal force of 15 kN/m. Design the section using M 25 grade concrete and Fe415 reinforcement. Sketch the crosssection. (5)
15. For general c φ soil, cohesion c is 50 kPa, the total unit weight γ_{t} is 20 kN/m^{3 }and the bearing capacity formula, calculate the net ultimate bearing capacity for a strip footing of width B = 2m at depth z = 1m. Considering shear failure only, estimate the safe total load on a footing 10 m long by 2 m wide strip footing using a factor of safety of 3. (5)
16. A soft normally consolidated clay layer is 20 m thick with a moisture content of 45%. The clay has a saturated unit weight of 20 kN/m^{3}, a particle specific gravity of 2.7 and a liquid limit of 60%. A foundation load will subjected the centre of the layer to a vertical stress increase of 10 kpa. Ground water level is at the surface of the clay. Estimate
(a) The initial and final effective stresses at the centre of the layer
(b) The approximate value of the compression index (C_{c})
(c) The consolidation settlement of the foundation if the initial effective stress at the centre of the soil is 100kPs.
Assume unit weight of water to be 10kN/m^{3}.
17. Estimate the safe load carrying capacity of a single bored pile 20m long, 500 mm diameter. The adhesion coefficient (d) is 0.4. Take a factor of safety of 2.5. The soil strata is as follows.
Depth (m) 
Soil deposit 
Undrained shear strength (S_{u})kPa 
05 
Loose fill 
50 
510 
Weathered over consolidate clay 
70 
1015 
Over consolidated clay 
100 
1530 
High overconsolidated clay 
200 
Assumne, φn=0 is valid and Nc=9, for deep fomadations. (5)
18. (a) What is the shear strength in terms of effective stress on a plane within a saturated soil mass at a point where the total normal stress is 295 kPa and the pore water pressure 120kPa? the effective stress shear strength parameters are C’=12 kPa and φ’ = 30^{0} (5)
(b) In a falling head permeameter test on a silty clay sample, the following results were obtained; sample length 120 mm; sample diameter 80 mm; initial head 1200 mm, final head 400 mm; time for fall in head 6 minutes stand pipe diameter 4 mm. Find the coefficient of permeability of the soil in mm/second.
19. Water flows through the Yjoint as shown in figure. Find the horizonal and vertical components of the force acting on the joint because of the flow of water. Neglet energy losses and body force.
20. Water flows in a rectangular channel at depth of 1.20 m and a velocity of 2.4m/sec. What would be the effect of a local rise in the channel bed of 0.60 m on the water surface ? (5)
21. A reservoir is proposed to be constructed to command an area of 1,20,000 hectares. The area has a monsoon rainfall of about 100cm per year. It is anticipated that sugar and rice would each be equal to 20% of the command area and wheat equal to 50% of the command area, making a total of annual irrigation equal to 90% of the command area.
(i) Work out the storage required for the reservoir, assuming the water requirements given below, canal losses as 25% of the head discharge and reservoir evaporation and dead storage losses as 20% of the gross capacity of the reservoir.
(ii) Determine also the full supply discharge of the canal at the head of the canal.
Crop 
Transplanted Rise 
Sugar Cane 
Wheat 
Sowing time 
July 
FebMar 
October 
Harvesting Time 
November Next year 
DecMarch 
MarApr 
Total Water Depth in cm 
150 
90 
37.5 
“Kor” period in weeks 
2.5 
4 
4 
“Kot” watering in cm 
19.0 
16.5 
13.5 
864B
Note that in which = Depth of water in cm, B=base period in
D
days, and D = duty of water in hectares/cumec. (5)
22. The following rainfall hyetograph and the corresponding direct run off are recorded in a watershed. Compute the onehour unit hydrography ordinates for the first four hours. Assume φ index = 0.50 cm/hr (5)
Time (hrs) 
Rainfall (cm) 
Direct Run Off (m^{3}/sec) 



1 
2.8 
64.2 
2 
5.2 
288.4 
3 
4.7 
794.5 
4 
0.0 
1369.6 
5 
0.0 
1593.7 
6 
0.0 
1175.1 
7 
0.0 
588.1 
8 
0.0 
286.9 
9 
0.0 
170.5 
10 
0.0 
110.0 
23. A dualmedia rapid sand filter plant is to be constructed for treatment of 72 million litres of water per day. A pilot plant study indicated that a filtration rate of 15m/h would be acceptable. Allowing one unit out of service for backwashing, how many 5mx8m filter units will be required ? Determine the net production in million litres per day of each filter unit if backwashing is done at 36m/h for 20 minutes and the water is wasted for the first 10 minutes of each filter run. (5)
24. The minimum flow of a river is 50m^{3}/s having a disoolved oxygen (DO) content of 7.0 mg/L (80% saturation) and BOD_{5} of 8.0 mg/L. It receives a waste water discharge of 5cm^{3}/s with BOD_{5} of 200 mg/L and no DO. If the rate constants for deoxygenation and reaeration (both base e) and 0.5/d and 1.0/d, respectively and the velocity of river flow is 0.8m/s, calculate the distance in kilometre downstream from the point of waste water discharge where the minimum DO occurs. (5)
25. An activated sludge aeration tank (length 30.0m; width 14.0m; effective liquid depth 4.3m) has the following parameters :
flow 0.0796m3, soluble BOD_{5} after primary settling 130 mg/L; mixed liquor suspended solids (MLSS) 2100 MG/L; mixed liquor volatile suspended solids (MLVSS) 1500 mg/L; 30 minute settled sludge volume 230 mL/L; and return sludge concentration 9100 mg/L. Determine the aeration period, food to microorganisms (F.M) ratio, sludge volume index (SVI), and return sludge rate. (5)
26. There is a horizontal curve of radius 360 m and length 180m. Calculate the clearance required from the central line on the inner side of the curve, so as to provide an overtaking sight distance of 250m. (5)
27. The width of expansion joint gap is 2.5 cm in a cement concrete 20 cm thick pavement. If the laying temperature is 15^{0} C and the maximum slab temperature in the summer is 55^{0}C, calculate
(i) the spacing between expansion joints, and
(ii) the spacing between contraction joints.
Coefficient of thermal expansion for concrete is 10×10^{6} per degree centigrade. Ultimate stress in tension in cement concrete is 1.6×10^{5} N/m^{2}. Ultimate tensile stress in steel is 1200x10N/m^{2}. Factor of safety is to be taken as 2. Assume the pavement width to be 3.5 m. Unit weight of steel is 75,000 N/m^{3}. Total reinforcement of 6kg/m^{2} is provided in the slab. (5)