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# GATE 2013 : Civil Engineering

17 pages, 65 questions, 52 questions with responses, 67 total responses
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2013 CIVIL ENGINEERING - CE Q. 1 Q. 25carries one mark each. Q.1 There is no value of x that can simultaneously satisfy both the given equations.Therefore, find the least squares error solution to the two equations, i.e., find the value of that minimizes the sum of squares of the errors in the two equations. __________ Q.2 What is the minimum number of multiplications involved in computing the matrix product PQR? Matrix has 4 rows and 2 columns, matrix has 2 rows and 4 columns, and matrix has 4 rows and 1 column. __________ Q.3 A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that a 1-h rainfall of magnitude 10 cm or more will occur in each oftwo successive years is: (A) 0.04 Q.4 0.2 (B) 1.0 (D) 0.0004 (C) 1.5 (D) 2.0 As per IS 800:2007, the cross-section in which the extreme fiber can reach the yield stress, but cannot develop the plastic moment of resistance due to failure by local buckling is classified as (A) plastic section (C) semi-compact section Q.6 (C)0.02 Maximum possible value of Compacting Factor for fresh (green) concrete is: (A) 0.5 Q.5 (B) (B) compact section (D) slender section The creep strains are (A) caused due to dead loads only (B) caused due to live loads only (C) caused due to cyclic loads only (D) independent of loads Q.7 As per IS 456:2000 for M20 grade concrete and plain barsin tension the design bond stress .Further, IS 456:2000 permits this design bond stress value to be increased by . Find the for HSD bars. The stress in theHSDreinforcing steel barsin tension, required development length, , for HSD barsin terms of the bar diameter, . __________ Q.8 The plane section remains plane assumption in bending theory implies: (A) strain profile is linear (B) stress profile is linear (C) both strain and stress profiles are linear (D)shear deformations are neglected CE 4/16

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2013 Q.9 CIVIL ENGINEERING - CE ) and Q (length and yield Two steel columns P (length and yield strength ) have the same cross-sections and end-conditions. The ratio of buckling strength load of column P to that of column Q is: (A) 0.5 Q.10 (B) 1.0 (C) 2.0 (D) 4.0 The pin-jointed 2-D truss is loaded with a horizontal force of at joint S and another vertical force at joint U, as shown.Find the force in member RS (in ) and report your answer taking tension as positive and compression as negative. __________ 4m 4m 4m R S 15 4m Q V U T 4m 15 W Q.11 A symmetric I-section (with width of each flange depth of web = 100 mm, and thickness of web . Find the magnitude of the shear stress(in flange. __________ Q.12 In its natural condition, a soil sample has a mass of and a volume of . After being completely dried in an oven, the mass of the sample is .Specific gravity is . Unit weight of water is . The degree of saturation of the soil is: (A) 0.65 Q.13 (B) 0.70 (C) 0.54 thickness of each flange , ) of steel is subjected to a shear force of in the web at its junction with the top (D) 0.61 The ratio Nf/Nd is known as shape factor, where Nf is the number of flow lines and Nd is the number of equipotential drops. Flow net is always drawn with a constant b/a ratio, where b and a are distances between two consecutive flow lines and equipotential lines, respectively. Assuming that b/a ratio remains the same, the shape factor of aflow net will change if the (A) upstream and downstream heads are interchanged (B) soil in the flow space is changed (C) dimensions of the flow space are changed (D) head difference causing the flow is changed CE 5/16

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2013 Q.14 CIVIL ENGINEERING - CE Following statementsare made on compacted soils, wherein DS stands forthe soils compacted on dry side of optimum moisture content and WS stands for thesoils compacted on wet side of optimum moisture content. Identify the incorrect statement. (A) Soil structure is flocculated onDS and dispersed on WS. (B) Construction pore water pressure is low on DS and high on WS. (C)On drying, shrinkage is high on DS and low on WS. (D)On access to water, swelling is high on DS and low on WS. Q.15 Four columns of a building are to be located within a plot size of 10 m x 10 m. The expected load on each column is 4000 kN. Allowable bearing capacity of the soil deposit is 100 kN/m2. The type of foundation best suited is (A) isolated footing (C) pile foundation Q.16 (B) raft foundation (D)combined footing For subcritical flow in an open channel, the control section for gradually varied flow profiles is (A) at the downstream end (C) at both upstream and downstream ends Q.17 (B) at the upstream end (D) at any intermediate section Group-I contains dimensionless parameters and Group- II contains the ratios. Group-I P. Mach Number Q. Reynolds Number R. Weber Number S. Froude Number Group -II 1. Ratio of inertial force and gravitational force 2. Ratio of fluid velocity and velocity of sound 3. Ratio of inertial force and viscous force 4. Ratio of inertial force and surface tension force The correct match of dimensionless parameters in Group- I with ratios in Group-II is: (A) P-3, Q-2, R-4, S-1 (C) P-2, Q-3, R-4, S-1 Q.18 (B) P-3, Q-4, R-2, S-1 (D) P-1, Q-3, R-2, S-4 For a two dimensional flow field, the stream function is given as 3 2 y x 2 . The 2 magnitude of discharge occurring between the stream lines passing through points (0,3) and (3,4) is: (A) Q.19 6 3 (C) 1.5 (D) 2 An isohyet is a line joining points of (A) equal temperature (C) equal rainfall depth CE (B) (B) equal humidity (D) equal evaporation 6/16

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2013 Q.20 CIVIL ENGINEERING - CE Some of the water quality parameters are measured by titrating a water sample with a titrant. Group-I gives a list of parameters and Group-IIgives the list of titrants. Group-I Group-II P.Alkalinity Q. Hardness R. Chloride S. Dissolved oxygen 1. N/35.5 AgNO3 2. N/40 Na2S2O3 3. N/50 H2SO4 4. N/50 EDTA The correct match of water quality parameters in Group-I with titrants in Group-II is: (A) P-1, Q-2, R-3, S-4 (C)P-2, Q-1, R-4, S-3 Q.21 (B)P-3, Q-4, R-1, S-2 (D) P-4, Q-3, R-2, S-1 A water treatment plant is designed to treat 1 m3/s of raw water. It has 14 sand filters. Surface area of each filter is 50 m2. What is the loading rate (in ) with two filters out of service for routine backwashing? __________ Q.22 Selectthe strength parameter of concrete usedindesign of plain jointed cement concrete pavements from the following choices: (A) Tensile strength (B) Compressive strength (C) Flexural strength (D) Shear strength Q.23 It was observed that 150 vehicles crossed a particular location of a highway ina duration of 30 minutes. Assuming that vehicle arrival follows a negative exponential distribution, find out the number of time headways greater than 5 seconds in the above observation? __________ Q.24 For two major roads with divided carriageway crossing at right angle,a full clover leaf interchange with four indirect ramps is provided. Following statements are made on turning movements of vehiclesto all directions from both roads. Identify the correct statement: (A) (B) (C) (D) Q.25 The latitude and departure of a line AB are +78 m and -45.1 m, respectively. The whole circle bearing of the line AB is: (A) 30 CE Merging from left is possible,butdiverging to left is notpossible. Both merging from left and diverging to left arepossible. Merging from left is not possible,butdiverging to left is possible. Neithermergingfrom left nordivergingto leftispossible. (B) 150 (C) 210 (D) 330 7/16

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2013 CIVIL ENGINEERING - CE Q. 26 to Q. 55 carry two marks each. Q.26 The state of 2D-stress at a point is given by the following matrix of stresses: What is the magnitude of maximum shear stressin MPa? (A) 50 Q.27 (B) 75 (C) 100 (D) 110 Find the magnitude of the error (correct to two decimal places) in the estimation of following integral using Simpson s x 4 4 0 1 Rule. Take the step length as 1. __________ 3 10 dx cos 6 Q.28 The solution for 3 sin 3 6 d is: 4 0 (A) 0 Q.29 (B) (C) 1 (D) 8 3 Find the value of such that the function f (x ) is a valid probability density function. __________ f ( x) ( x 1)(2 x) 0 Q.30 1 15 for 1 x 2 otherwise Laplace equation for water flow in soils is given below. 2H 2H 2H 0 z 2 y 2 x 2 Head H does not vary in y and z directions. Boundary conditions are: at x = 0, H = 5;and dH 1 . dx What is the value of H at x = 1.2? __________ CE 8/16

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2013 Q.31 CIVIL ENGINEERING - CE All members in the rigid-jointed frame shown are prismatic and have the same flexural stiffness Find the magnitude of the bending moment at Q (in ) due to the given loading. __________ 3m . 4m S 2m T P R 100 kNm 2m Q Q.32 A uniform beam and free at the end in the form of a quarter-circle of radius is fixed at end is applied as shown. The vertical downward displacement, , where a load , at the loaded point places). __________ . Find the value of is given by: (correct to 4-decimal Q W R P CE 9/16

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2013 CIVIL ENGINEERING - CE E Q.33 u beam m weighing is su upported at E and F by cable ABCD. Determine the tension A uniform (in in segme ent AB of thi is cable (corr rect to 1-dec cimal place). Assume the e cables ABC CD, BE and _____ CF to be weightless. ______ Q.34 am ha as internal hi inges in span ns and as shown n. The beam mmay be sub bjected to a Bea moving distribu uted vertical l load of ma aximum intensity of any le ength anywh here on the bea am. The ma aximum abso olute value of o the shear force f (in ) that can oc ccur due to this t loading just t to the right of support Q shall be: Q P 5m (A A) 30 Q.35 CE R 20 m 5m (B B) 40 (C) 45 S 5m 5m ( (D) 55 deep is pre-stresse A rectangular r c concrete beam m w wide and ed by means s of 16 high tensile wires, each e of 7 mm m diameter, located at m the bottom m face of th he beamat a from ven section. If the effective pre-stre ess in the wires is , what is the maximu um sagging giv ben nding momen nt (in ) (correct to 1-decimal 1 pla ace) due to live l loadthat this sectiono of the beam can n withstand without w caus sing tensile stress s at the bottom face of the beam m? Neglect th he effect of dea ad load of beam. _______ ____ 10/16 6

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2013 Q.36 CIVIL ENGINEERING - CE The soil profile below a lake with water level at elevation m and lake bottom at elevation m is shown in the figure, where k is the permeability coefficient. A piezometer (stand pipe) installed in the sand layer shows a reading of +10 m elevation. Assume that thepiezometric headis uniform in the sand layer. The quantity of water (in m3/s) flowing into the lake from the sand layer through the silt layer per unit area of the lake bed is: Stand pipe +10 0 Lake Lake bottom -10 Silt (k = 10-6 m/s) -30 Sand -40 (under artesian pressure) Rock (A) 1.5 x 10-6 (C) 1.0 x 10-6 Q.37 The soil profile above the rock surface for a 25oinfinite slope is shown in the figure, where su is the undrained shear strength and t is total unit weight. The slip will occur at a depth of (A) 8.83 m CE (B) 2.0 x 10-6 (D) 0.5 x 10-6 (B) 9.79 m (C) 7.83 m (D) 6.53 m 11/16

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2013 Q.38 CIVIL ENGINEERING - CE Two different soil types (Soil 1 and Soil 2) are used as backfill behind a retaining wall as shown in the figure, where t is total unit weight, and c' and ' are effective cohesion and effective angle of shearing resistance. The resultant active earth forceper unit length (in kN/m) acting on the wall is: Retaining wall 2 m 2 m (A) 31.7 Q.39 20.1 (D) 57.0 (B)0.35 (C) 2.52 (D) 1.25 (B) 15.4 (C) 10.5 (D) 17.2 The transplantation of rice requires 10 days and total depth of water required during transplantation is 48 cm. During transplantation, there is an effective rainfall (useful for irrigation) of 8 cm. The duty of irrigation water (in hectares/cumec) is: (A) 612 Q.42 (C) 51.8 The normal depth in a wide rectangular channel is increased by 10%. The percentage increase in the discharge in the channel is: (A) Q.41 Soil 2: t = 20 kN/m3; c' = 0; ' = 40o A 2 km long pipe of 0.2 m diameter connects two reservoirs. The difference between water levels in the reservoirs is 8 m. The Darcy-Weisbachfriction factor of the pipe is 0.04. Accounting for frictional, entry and exit losses, the velocity in the pipe (in m/s) is: (A) 0.63 Q.40 (B) 35.2 Soil 1: t = 15 kN/m3; c' = 0; ' = 30o (B) 216 (C)300 (D) 108 A settling tank in a water treatment plant is designed for a surface overflow rate of30 . 3 Assumespecific gravity of sedimentparticles = 2.65, density of water ( ) = 1000 kg/m , dynamic viscosity of water ( )=0.001 N.s/m2,and Stokes lawisvalid.The approximate minimum size of particles that would be completely removed is: (A) 0.01mm Q.43 CE (B) 0.02 mm(C) 0.03 mm(D) 0.04 mm A student began experiment for determination of 5-day, 20 C BOD on Monday. Since the 5thday fell on Saturday, the final DO readings were taken on next Monday. On calculation, BOD (i.e. 7 day, 20 C) was found to be 150 mg/L. What would be the5-day, 20 C BOD (in mg/L)? Assume value of BOD rate constant (k) at standard temperature of 20 C as 0.23/day (base e). __________ 12/16

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2013 Q.44 CIVIL ENGINEERING - CE Elevation and temperature data for a place are tabulated below: Elevation, m 4 444 Temperature, C 21.25 15.70 Based on the above data, lapse rate can be referred as: (A) Super-adiabatic Q.45 (C) Sub-adiabatic (D) Inversion The percent voids in mineral aggregate (VMA) and percent air voids (Vv) in a compacted cylindrical bituminous mix specimen are 15 and 4.5respectively. The percent voids filled with bitumen (VFB) for this specimen is: (A) 24 Q.46 (B) Neutral (B) 30 (C) 54 (D) 70 Following bearings are observed while traversing with a compass. Line AB BC CD DE EA Fore Bearing 126 45 49 15 340 30 258 30 212 30 Back Bearing 308 00 227 30 161 45 78 30 31 45 After applying the correction due to local attraction, the corrected fore bearing of line BC will be: (A) 48 15 Q.47 (B)50 15 (C) 49 45 (D) 48 45 A theodolite is set up at station A and a 3 m long staff is held vertically at station B. The depression angle reading at 2.5 m marking on the staffis 6 10 . The horizontal distance between A and B is 2200 m. Height of instrument at station A is 1.1 m and R.L. of A is 880.88 m.Apply the curvature and refraction correction, and determine the R.L. of B (in m). __________ Common Data Questions Common Data for Questions 48 and 49: A propped cantilever made of a prismatic steel beam is subjected to a concentrated load P at mid span as P shown. R 1.5m Q.48 If load __________ Q.49 If the magnitude of load is increased till collapse and the plastic moment carrying capacity of steel beam section is , determine reaction (in )(correct to 1-decimal place) using plastic analysis. __________ CE 1.5m ,find the reaction (in ) (correct to 1-decimal place)using elastic analysis. 13/16

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2013 CIVIL ENGINEERING - CE Common Data for Questions 50 and 51: For a portion of national highway where a descending gradient of 1 in 25 meets with an ascending gradient of 1 in 20, a valley curve needs to be designed for a vehicle travelling at 90 kmphbased on the following conditions. (i) (ii) headlight sight distance equalto the stopping sight distance (SSD) of a level terrain consideringlength of valley curve> SSD. comfort condition with allowablerate of change of centrifugal acceleration = 0.5 m/sec3. Assume total reaction time = 2.5 seconds; coefficient of longitudinal friction of the pavement= 0.35; height of head light of the vehicle =0.75 m; andbeam angle = 1 . Q.50 What is the length of valley curve (in m) based on the head light sight distance condition? __________ Q.51 What is the length of valley curve (in m)based on the comfort condition? __________ Linked Answer Questions Statement for Linked Answer Questions 52 and 53: A multistory building with a basement is to be constructed. The top 4 m consists of loose silt, below which dense sand layer is present up to a great depth. Ground water table is at the surface. The foundation consists of the basement slab of 6 m width which will rest on the top of dense sand as shown in the figure. For dense sand, saturated unit weight = 20kN/m3, and bearing capacity factors Nq = 40 and N = 45. For loose silt, saturated unit weight = 18kN/m3, Nq = 15 and N = 20.Effective cohesion c' is zero for both soils.Unit weight of water is 10 kN/m3. Neglect shape factor and depth factor. Average elastic modulus E and Poisson s ratio of dense sand is 60 x 103kN/m2 and 0.3 respectively. Ground surface Loose silt 4 m Loose silt Basement Foundation slab 6 m Dense sand Q.52 Using factor of safety = 3, the net safe bearing capacity (in kN/m2) of the foundation is: (A) 610 Q.53 (C) 983 (D) 693 The foundation slab is subjected to vertical downward stresses equal to net safe bearing capacity derived in the above question. Using influence factor If = 2.0, and neglecting embedment depth and rigidity corrections, the immediate settlement of the dense sand layer will be: (A) 58 mm CE (B) 320 (B) 111 mm (C) 126 mm (D) 179 mm 14/16

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2013 CIVIL ENGINEERING - CE Statement for Linked Answer Questions 54 and 55: At a station, Storm I of 5 hour duration with intensity 2 cm/h resulted in a runoff of 4 cm and Storm II of 8 hour duration resulted in a runoff of 8.4 cm. Assume that the -index is the same for both the storms. Q.54 The -index (in cm/h) is: (A)1.2 Q.55 (B)1.0 (C)1.6 (D) 1.4 (C)1.50 (D)2.25 The intensity of storm II (in cm/h) is: (A) 2.00 (B)1.75 General Aptitude (GA) Questions Q. 56 Q. 60 carry one mark each. Q.56 A number is as much greater than 75 as it is smaller than 117. The number is: (A) 91 Q.57 (C) 89 (D) 96 The professor ordered to the students to go out of the class. I II III IV Which of the above underlined parts of the sentence is grammatically incorrect? (A) I Q.58 (B) 93 (B) II (C) III (D) IV Which of the following options is the closest in meaning to the word given below: Primeval (A) Modern (C) Primitive Q.59 (B) Historic (D) Antique Friendship, no matter how _________it is, has its limitations. (A) cordial (B) intimate (C) secret (D) pleasant Q.60 Select the pair that best expresses a relationship similar to that expressed in the pair: Medicine: Health (A) Science: Experiment (C) Education: Knowledge CE (B) Wealth: Peace (D) Money: Happiness 15/16

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2013 CIVIL ENGINEERING - CE Q. 61 to Q. 65 carry two marks each. Q.61 X and Y are two positive real numbers such that following values of the function and . For which of the will give maximum value? (A) (4/3, 10/3) (B) (8/3, 20/3) (C) (8/3, 10/3) (D) (4/3, 20/3) Q.62 If (A) 2, 1/3 Q.63 then the values of is: (B) 1/2, 3 (C) 3/2, 9 (D) 2/3, 9 Following table provides figures (in rupees) on annual expenditure of a firm for two years - 2010 and 2011. Category 2010 2011 Raw material 5200 6240 Power & fuel 7000 9450 Salary & wages 9000 12600 Plant & machinery 20000 25000 Advertising 15000 19500 Research & Development 22000 26400 In 2011, which of the following two categories have registered increase by same percentage? (A) Raw material and Salary & wages (B) Salary & wages and Advertising (C) Power & fuel and Advertising (D) Raw material and Research & Development Q.64 A firm is selling its product at Rs. 60 per unit. The total cost of production is Rs. 100 and firm is earning total profit of Rs. 500. Later, the total cost increased by 30%. By what percentage the price should be increased to maintained the same profit level. (A) 5 Q.65 (B) 10 (C) 15 (D) 30 Abhishek is elder to Savar. Savar is younger to Anshul. Which of the given conclusions is logically valid and is inferred from the above statements? (A) Abhishek is elder to Anshul (B) Anshul is elder to Abhishek (C) Abhishek and Anshul are of the same age (D) No conclusion follows END OF THE QUESTION PAPER CE 16/16

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GATE 2013 : Answer keys for CE - Civil Engineering Paper Q.No Key(s)/Value(s) Paper Q.No Key(s)/Value(s) CE 1 0.5 CE 36 D CE 2 16 CE 37 A CE 3 D CE 38 A CE 4 B CE 39 A CE 5 C CE 40 D CE 6 A CE 41 B CE 7 46 to 47 CE 42 B CE 8 A CE 43 127 to 132 CE 9 D CE 44 A CE 10 0 CE 45 D CE 11 70 to 72 CE 46 D CE 12 C CE 47 641.9 to 642.3 CE 13 C CE 48 25 CE 14 C CE 49 60 CE 15 C CE 50 308 to 311 CE 16 A CE 51 106 to 107 CE 17 C CE 52 Marks to All CE 18 B CE 53 Marks to All CE 19 C CE 54 A CE 20 B CE 55 D CE 21 143 to 145 CE 56 D CE 22 C CE 57 B CE 23 Marks to All CE 58 C CE 24 B CE 59 B CE 25 D CE 60 C CE 26 A CE 61 A CE 27 0.52 to 0.55 CE 62 B CE 28 B CE 63 D CE 29 6 CE 64 A CE 30 3.8 CE 65 D CE 31 25 CE 32 0.785 to 0.786 CE 33 1310 to 1313 CE 34 C CE 35 85.5 to 86.5

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